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Symbols * (multiplication) operator in matrix operations, Matrix Multiplication: The * Operator , Scalar Multiplication: The * Operator , Vector Multiplication: The * Operator in quaternion operations, Quaternion multiplication: The * operator , Vector multiplication: The * operator , Quaternion Multiplication: The * Operator , Scalar Multiplication: The * Operator , Vector Multiplication: The * Operator in vector operations, Vector Dot Product: The * Operator , Scalar Multiplication: The * Operator *= (multiplication) operator in matrix operations, Scalar Multiplication: The *= Operator in quaternion operations, Scalar Multiplication: The *= Operator in vector operations, Scalar Multiplication: The *= Operator + (addition) operator in matrix operations, Matrix Addition: The + Operator in quaternion operations, Quaternion Addition: The + Operator in vector operations, Vector Addition: The + Operator += (addition) operator in matrix operations, Matrix Addition: The += Operator in quaternion operations, Quaternion Addition: The += Operator in vector operations, Vector Addition: The += Operator / (division) operator in matrix operations, Scalar Divide: The / Operator in vector operations, Scalar Division: The / Operator /= (division) operator in matrix operations, Scalar Division: The /= Operator in quaternion operations, Scalar Division: The /= Operator , Scalar Division: The / Operator in vector operations, Scalar Division: The /= Operator ^ (cross-product) operator, in vector operations, Vectors , Vector Cross Product: The ^ Operator ~ (conjugate) operator in quaternion operations, Conjugate: The ~ operator , Conjugate: The ~ Operator − (conjugate) operator in vector operations, Conjugate: The − Operator − (subtraction) operator in matrix operations, Matrix Subtraction: The − Operator in quaternion operations, Quaternion Subtraction: The − Operator in vector operations, Vector Subtraction: The − Operator −= (subtraction) operator in matrix operations, Matrix Subtraction: The −= Operator in quaternion operations, Quaternion Subtraction: The −= Operator in vector operations, Vector Subtraction: The −= Operator A Abbott, Ira H., Lift and Drag acceleration about, Velocity and Acceleration accelerometer theory on, Accelerometer Theory angular, Units and Measures , Angular Velocity and Acceleration –Angular Velocity and Acceleration , Rigid-Body Kinetics average, Velocity and Acceleration centrifugal, Steering centripetal, Angular Velocity and Acceleration , Steering constant, Constant Acceleration –Constant Acceleration equations for, Particle Kinetics in 2D equations of motion and, Particle Kinetics in 2D instantaneous, Velocity and Acceleration linear, Newton’s Laws of Motion , Units and Measures , Units and Measures , Newton’s Second Law of Motion , Force and Torque , Calculating Forces nonconstant, Nonconstant Acceleration relative, Angular Velocity and Acceleration rotational, Force and Torque second derivatives of, Velocity and Acceleration tangential, Angular Velocity and Acceleration velocity and, Velocity and Acceleration –Velocity and Acceleration acceleration vector, computing, Newton’s Second Law of Motion , Numerical Differentiation accelerometers about, Accelerometers –Accelerometer Theory common specifications, Common Accelerometer Specifications controlling sprites example, Using Tilt to Control a Sprite –Two Degrees of Freedom data clipping, Data Clipping digital, Kinetics MEMS, Accelerometer Theory –MEMS Accelerometers sensing orientation with, Simple Particle Model , Sensing Orientation sensing tilt, Sensing Tilt –Two Degrees of Freedom active stereoization, Programming Considerations –Active Stereoization ACVs (air cushion vehicles) (see hovercraft) adaptive step size method, Euler’s Method addition (+) operator in matrix operations, Matrix Addition: The + Operator in quaternion operations, Quaternion Addition: The + Operator in vector operations, Vector Addition: The + Operator addition (+=) operator in matrix operations, Matrix Addition: The += Operator in quaternion operations, Quaternion Addition: The += Operator in vector operations, Vector Addition: The += Operator aerodynamic drag in billiards example, Calculating Forces in cars, Resistance on hovercraft, Force Effectors , Resistance –Resistance aerostatic lift, How Hovercraft Work ailerons, in aircraft, Flight Controls , Geometry , Control aim (guns) breathing and body position, Breathing and Body Position –Breathing and Body Position defined, Projectile Motion elevation adjustments, Bullet drop: Gravity and air resistance shooting positions, Breathing and Body Position taking aim, Taking Aim zeroing the sights, Zeroing the Sights –Wind air cushion vehicles (ACVs) (see hovercraft) air drag particle simulation, Implementing External Forces for ships and boats, General Resistance shooting guns example, Drag aircraft control surfaces in, Geometry controlling, Control flight controls in, Rotation in 3D Rigid-Body Simulators , Flight Controls –Flight Controls forces acting on, Aircraft , Lift and Drag –Other Forces geometry of, Geometry modeling, Modeling –Modeling parts of, Geometry quaternion operations in, Quaternions in 3D Simulators –Quaternions in 3D Simulators weather helm and, Resistance airfoil about, Geometry lift and drag forces, Lift and Drag –Lift and Drag stalled, Lift and Drag alpha (opacity), Optical Tracking altitude barometers and, Barometers defined, Gaming from One Place to Another gravity and, Force Fields trilateration technique and, Two-Dimensional Mathematical Treatment anaglyphs, complementary-color, Complementary-Color Anaglyphs Anderson, Byron, Propulsion angle of attack critical, Lift and Drag defined, Geometry lift and drag forces, Lift and Drag in lift and drag, Lift and Drag stalls and, Lift and Drag angular acceleration angular velocity and, Angular Velocity and Acceleration –Angular Velocity and Acceleration rigid-body kinetics and, Rigid-Body Kinetics units and symbols for, Units and Measures angular displacement, Angular Velocity and Acceleration , Angular Velocity and Acceleration angular effects in collision response, Angular Effects –Angular Effects angular impulse in collisions, Linear and Angular Impulse –Linear and Angular Impulse golf example, Friction in impulse-momentum principle, Impulse-Momentum Principle angular kinetic energy, Impact angular momentum equation for, Inertia Tensor laws of motion and, Newton’s Second Law of Motion angular motion defined, Mass, Center of Mass, and Moment of Inertia particle explosions and, Particle Explosions rigid-body kinetics and, Rigid-Body Kinetics –Rigid-Body Kinetics angular velocity angular acceleration and, Angular Velocity and Acceleration –Angular Velocity and Acceleration Euler integration and, Integration laws of motion and, Newton’s Second Law of Motion rotation in 3D rigid-body simulation and, Rotation Matrices , Quaternions units and symbols for, Units and Measures anisotropic materials, Newton’s Second Law of Motion antipodal locations, Distance Archimedes’ principle of buoyancy, Stability arm rod (golf swings), Modeling a Golf Swing aspect ratio, aircraft wing area, Geometry atan function, Using Tilt to Control a Sprite atan2 function, Great-Circle Heading atmospheric pressure, Under Pressure , Barometers atomic clock drift, Two-Dimensional Mathematical Treatment attentuation in sound, Attenuation automobiles (see cars) autosterescopy, Autostereoscopy average acceleration, Velocity and Acceleration B backward difference scheme, Numerical Differentiation ballistic coefficient (BC), Projectile Motion ballistics and firearms, Projectile Motion (see also shooting guns example) about, Projectile Motion particle explosions, Particle Explosions –Particle Explosions projectile motion, Projectile Motion –Projectile Motion recoil and impact, Recoil and Impact taking aim, Taking Aim –Breathing and Body Position Bancroft, Stephen, Two-Dimensional Mathematical Treatment barometers, Pressure Sensors and Load Cells , Barometers –Barometers baseball examples collisions in, Impact –Impact Magnus effect in, Magnus Effect BC (ballistic coefficient), Projectile Motion Bernouilli, David, Drag Bernoulli’s equation, Drag , Lift and Drag billiards about, Billiards –Billiards calculating forces, Calculating Forces –Calculating Forces collision example, Impact –Impact handling collisions, Handling Collisions –Handling Collisions implementing example, Implementation –Implementation initializing example, Initialization –Stepping the Simulation stepping simulation, Stepping the Simulation binaural recording, How We Hear in 3D binocular disparity, Binocular Vision binocular rivalry, Complementary-Color Anaglyphs binocular vision, Binocular Vision –Binocular Vision biomechanics, Sports , Sports (see also sports) boats (see ships and boats) Borst, Henry V., Lift and Drag boundary layer in fluid dynamic drag, Drag , Virtual mass bounding boxes, Collision Detection bounding circle check, Linear Collision Response , Angular Effects bounding spheres, Collision Detection Bourg, David M., Particles Bradski, Gary, OpenCV breadth-to-draft ratio, General Resistance breadth-to-length ratio, Virtual mass buoyancy about, Buoyancy –Buoyancy calculating, Buoyancy pressure and, Buoyancy in ship stability, Stability buttons, pressure-sensitive, Button Mashing –Button Mashing C cannon ball game example (see shooting guns example) capacitive touch screens, Capacitive , Capacitive Touch Screens –Mutual capacitance capsizing ships and boats, Stability , Sinking cars about, Cars power and, Power resistance and, Resistance steering, Steering –Steering stopping distance in, Stopping Distance Cartesian coordinate system about, Coordinate System 2D particle
kinematics and, 2D Particle Kinematics Cavendish, Henry, Force Fields cavitation, Propulsion center of gravity (see center of mass) center of mass calculating, Mass, Center of Mass, and Moment of Inertia –Mass, Center of Mass, and Moment of Inertia defined, Mass, Center of Mass, and Moment of Inertia impact and, Impact load cells and, Center of gravity –Center of gravity local coordinate system and, Local Coordinate Axes quaternion rotation and, Quaternions rigid-body kinematics and, Rigid-Body Kinematics in ship stability, Stability torque and, Force and Torque 2D example, Mass, Center of Mass, and Moment of Inertia center of percussion, Impact center of pressure, Force Effectors central difference, second-order, Numerical Differentiation central impact, Impact , Linear Collision Response centrifugal acceleration, Steering centripetal acceleration, Angular Velocity and Acceleration , Steering chord length, aircraft wings, Geometry chord line, Geometry circular cylinder, mass moment of inertia formula, Mass, Center of Mass, and Moment of Inertia circular cylindrical shell, mass moment of inertia formula, Mass, Center of Mass, and Moment of Inertia circular polarization of light, Linear and Circular Polarization –Linear and Circular Polarization cloth simulation, Connecting Objects coefficient of restitution applying formula for, Impact collision response and, Collision Response defined, Impact physics models and, Physics Models coefficient of rolling resistance, Resistance coefficients of friction, Friction , Physics Models collision detection about, Collisions , Linear Collision Response , Collision Detection billiards example, Handling Collisions –Handling Collisions bounding circle check, Linear Collision Response , Angular Effects collision response and, Collision Response continuous, Collision Detection particle-to-ground, Particle-to-Ground Collisions –Particle-to-Ground Collisions particle-to-obstacle, Particle-to-Obstacle Collisions –Particle-to-Obstacle Collisions physics engines and, Building Your Own Physics Engine , Collision Detection vertex-edge collisions, Angular Effects –Angular Effects vertex-vertex collisions, Angular Effects –Angular Effects collision response about, Collisions angular effects in, Angular Effects –Angular Effects billiards example, Handling Collisions –Handling Collisions collision detection and, Collision Response conservation of momentum principle, Impact , Impact , Recoil and Impact implementing, Implementing Collision Response –Angular Effects impulse-momentum principle, Impulse-Momentum Principle , Collision Response linear, Linear Collision Response –Linear Collision Response particle-to-ground, Particle-to-Ground Collisions –Particle-to-Ground Collisions particle-to-obstacle, Particle-to-Obstacle Collisions –Particle-to-Obstacle Collisions physics engines and, Building Your Own Physics Engine , Collision Response collisions about, Collisions angular impulse in, Linear and Angular Impulse –Linear and Angular Impulse , Friction baseball and bat example, Impact –Impact billiard ball example, Impact –Impact , Billiards friction and, Friction –Friction golf example, Friction –Friction handling in billiards example, Handling Collisions –Handling Collisions impact force and, Impact –Impact implementing in particle simulation, Implementing Collisions –Particle-to-Obstacle Collisions impulse-momentum principle, Impulse-Momentum Principle , Collision Response inelastic, Impact line of action of, Impact linear impulse in, Linear and Angular Impulse –Linear and Angular Impulse , Linear Collision Response penetration in, Linear Collision Response , Linear Collision Response , Collision Response plastic, Impact compartments in ships and boats, Sinking complementary-color anaglyphs, Complementary-Color Anaglyphs condensation, What Is Sound? condition table, motion-identifying, Center of gravity conjugate operator in quaternion operations, Conjugate: The ~ operator , Conjugate: The ~ Operator in vector operations, Conjugate: The − Operator connecting objects about, Connecting Objects connecting particles, Connecting Particles –Update the simulation connecting rigid bodies, Connecting Rigid Bodies –Rotational Restraint hanging rope or vine example, Connecting Particles –Update the simulation linked-chain example, Connecting Rigid Bodies –Rotational Restraint conservation of momentum principle, Impact , Impact , Recoil and Impact constant acceleration, Constant Acceleration –Constant Acceleration contact forces about, Forces in billiards example, Calculating Forces center of mass and, Force and Torque collision response and, Collision Response friction as, Friction –Friction contact manifold, Collision Detection , Handling Collisions continuous collision detection, Collision Detection convergence distance, The Left and Right Frustums , Active Stereoization conversion functions, in quaternion operations, Conversion Functions coordinate systems accelerometer example, Sensing Orientation Cartesian, Coordinate System , 2D Particle Kinematics in particle simulation, Simple Particle Model geographic, Gaming from One Place to Another , Two-Dimensional Mathematical Treatment local, Local Coordinate Axes rotating, Rotation Matrices 3D rigid-body simulation, 3D Rigid-Body Simulator coordinate transformation, 2D rigid-body
simulation, Transforming Coordinates coupled motions, Ship Motions , Coupled Motions critical attack angle, Lift and Drag cross track error, Rhumb Line cross-product (^) operator, in vector operations, Vectors , Vector Cross Product: The ^ Operator D dampers about, Springs and Dampers connecting objects, Springs and Dampers equation for, Springs and Dampers , Springs and Dampers uses for, Springs and Dampers data clipping in accelerometers, Data Clipping degrees of freedom controlling sprites example, Two Degrees of Freedom –Two Degrees of Freedom rigid bodies and, Rotation in 3D Rigid-Body Simulators , Sensing Orientation ships and boats, Sinking , Ship Motions –Pitch DegreesToRadians function, Conversion Functions density sound and, What Is Sound? uniform, Rigid-Body Kinetics units and symbols for, Units and Measures , Units and Measures depth from focus (cameras), Kinect derivatives defined, Derivatives and Integrals second, Velocity and Acceleration determinant, in matrix operations, Determinant differentiation schemes (optical tracking), Numerical Differentiation –Numerical Differentiation digital accelerometers, Kinetics digital signal processing, Accelerometers dihedral angle, Modeling direct central impact, Impact direct force effectors, Force Effectors direct impact, Impact direction acceleration and, Newton’s Second Law of Motion in vector operations, Vectors of rotation, Angular Velocity and Acceleration , Force and Torque tensors and, Newton’s Second Law of Motion velocity and, Velocity and Acceleration , X Components –X Components wind, Particle Kinetics in 3D direction angles, Magnitude direction cosines, vector, X Components , Magnitude disparity maps, OpenCV dispersive signal technology, Exotic: Dispersive Signal and Surface Acoustic Wave displacement about, Velocity and Acceleration , Ships and Boats accelerometer theory on, Accelerometer Theory angular, Angular Velocity and Acceleration , Angular Velocity and Acceleration distance traveled versus, Velocity and Acceleration formula for, Constant Acceleration volume of ships and, Stability weight of ship and, Stability distance calculating between latitude and longitude
coordinates, Location, Location, Location –Rhumb Line convergence, The Left and Right Frustums , Active Stereoization equations of motion and, Particle Kinetics in 2D intraocular, Active Stereoization skidding, Stopping Distance stopping, Stopping Distance distance tolerance, Linear Collision Response , Collision Response distance traveled displacement versus, Velocity and Acceleration equations for, Particle Kinetics in 2D second derivatives of, Velocity and Acceleration time and, Velocity and Acceleration division (/) operator in matrix operations, Scalar Divide: The / Operator in vector operations, Scalar Division: The / Operator division (/=) operator in matrix operations, Scalar Division: The /= Operator in quaternion operations, Scalar Division: The /= Operator , Scalar Division: The / Operator in vector operations, Scalar Division: The /= Operator Doppler effect, Speed of Sound , Doppler Effect dot-product (*) operator, Vectors , Vector Dot Product: The * Operator drag coefficient aircraft and, Other Forces calculating, Drag cars and, Resistance fluid dynamic drag and, Fluid Dynamic Drag hovercraft and, Resistance physics models and, Physics Models terminal velocity and, Drag drag forces aircraft in flight and, Aircraft , Lift and Drag –Lift and Drag , Other Forces on cars, Resistance fluid dynamic, Fluid Dynamic Drag on hovercraft, Resistance –Resistance nonconstant acceleration and, Nonconstant Acceleration particle kinetics in 3D, Particle Kinetics in 3D resistance in ships and, General Resistance –General Resistance speed and, Drag viscous, Fluid Dynamic Drag E Einstein, Albert, Relativistic Time , Accelerometer Theory electromagnetic waves, Linear and Circular Polarization elevators, in aircraft, Flight Controls , Control engineering strain, Tiny scales equal and opposite forces, Springs and Dampers , Numerical Integrator equations of motion defined, Kinetics linked-chain example, Update numerical integrators and, Numerical Integrator particle kinetics in 2D, Particle Kinetics in 2D –Particle Kinetics in 2D particle kinetics in 3D, Particle Kinetics in 3D in particle simulation, Integrator real-time simulations and, Integrating the Equations of Motion –Integrating the Equations of Motion in 2D rigid-body
simulation, Transforming Coordinates Euler angles constructing quaternions from, MakeQFromEulerAngles , MakeQFromEulerAngles extracting from quaternions, MakeEulerAnglesFromQ , Integration , MakeEulerAnglesFromQ steering cars and, Steering in 3D motion, Local Coordinate Axes , Rotation in 3D Rigid-Body Simulators Euler’s method for billiards example, Stepping the Simulation improved, Better Methods –Better Methods modeling golf swings, Solving the Golf Swing Equations in particle simulation, Integrator in real-time
simulations, Euler’s Method –Euler’s Method in 3D rigid-body simulation, Integration in 2D rigid-body
simulation, Integrator exotic touch screens technologies, Exotic: Dispersive Signal and Surface Acoustic Wave explosions about, Explosions kinematic particle explosion, Kinematic Particle Explosion –Kinematic Particle Explosion kinematic particle explosions, Particle Explosions –Particle Explosions particle, Particle Explosions –Particle Explosions polygon, Polygon Explosions –Polygon Explosions external ballistics, Projectile Motion F fade effect, Kinematic Particle Explosion far zero, Bullet drop: Gravity and air resistance field forces about, Forces , Force Fields center of mass and, Force and Torque filters accelerometers and, Accelerometers polarized light and, Linear and Circular Polarization in 3D sound, How We Hear in 3D firearms (see ballistics and firearms) fireworks exploding, Kinematic Particle Explosion flag model, Connecting Objects flaps, in aircraft, Flight Controls , Geometry , Lift and Drag , Control flight controls, 3D rigid-body simulation, Rotation in 3D Rigid-Body Simulators , Flight Controls –Flight Controls , Modeling –Modeling flight simulation (see aircraft) fluid dynamic drag about, Fluid Dynamic Drag around a sphere, Drag –Drag boundary layer in, Drag , Virtual mass drag coefficient, Fluid Dynamic Drag , Drag laminar flow, Fluid Dynamic Drag in projectiles, Drag –Drag Reynolds number, Drag separation point in, Drag of spinning sphere, Magnus Effect turbulent flow, Fluid Dynamic Drag turbulent wake, Drag football simulation game, Kinematic Particle Explosion force about, Forces aggregating, Numerical Integrator on aircraft in flight, Aircraft , Lift and Drag –Other Forces buoyancy, Buoyancy –Buoyancy calculating in billiards example, Calculating Forces –Calculating Forces equal and opposite, Springs and Dampers , Numerical Integrator fluid dynamic drag, Fluid Dynamic Drag impact, Impact –Impact impulse, Impulse-Momentum Principle linear acceleration and, Force and Torque Newton’s second law of motion and, Newton’s Laws of Motion , Newton’s Second Law of Motion pressure versus, Pressure springs and dampers, Springs and Dampers static, Friction torque versus, Force and Torque –Force and Torque units and symbols for, Units and Measures , Units and Measures force effectors, Force Effectors forces at a distance, Forces , Force Fields forward azimuth, Great-Circle Heading FourSquare app, Mixed Reality frequency measuring for accelerometers, Accelerometers measuring for sound, What Is Sound? friction about, Friction –Friction in billiards example, Calculating Forces calculating, Friction coefficients of, Friction collisions and, Friction –Friction recoil and, Recoil and Impact skidding distance and, Stopping Distance frictional drag aircraft and, Other Forces Bernouilli’s equation and, Drag moving through fluid and, Units and Measures , General Resistance frustum, viewing, The Left and Right Frustums –The Left and Right Frustums fuselage, in aircraft, Geometry fusion in binocular vision, Binocular Vision G game engines, Building Your Own Physics Engine , Aircraft geocaching, Geocaching and Reverse Geocaching geographic coordinate system, Gaming from One Place to Another , Two-Dimensional Mathematical Treatment Gillespie, Thomas, Steering Global Positioning System (GPS) about, Gaming from One Place to Another , What Time Is It? , Barometers calculating between latitude and longitude, Location, Location, Location –Rhumb Line location-based gaming and, Location-Based Gaming trilateration technique, Two-Dimensional Mathematical Treatment –Two-Dimensional Mathematical Treatment GM (stability index), Stability golf examples in collisions, Friction –Friction Magnus effect in, Magnus Effect modeling golf swings, Modeling a Golf Swing –Solving the Golf Swing Equations physics engine considerations, Building Your Own Physics Engine two-rod model, Modeling a Golf Swing Google Maps, Barometers GPS (Global Positioning System) about, Gaming from One Place to Another , What Time Is It? , Barometers calculating between latitude and longitude, Location, Location, Location –Rhumb Line location-based gaming and, Location-Based Gaming trilateration technique, Two-Dimensional Mathematical Treatment –Two-Dimensional Mathematical Treatment gravitational force accelerometer theory on, Accelerometer Theory aircraft in flight and, Aircraft as force effector, Force Effectors Newton’s law of grativation, Force Fields particle simulation and, Simple Particle Model –Simple Particle Model projectiles and, Projectiles zeroing the sights and, Bullet drop: Gravity and air resistance –Bullet drop: Gravity and air resistance great-circle heading, Location, Location, Location , Great-Circle Heading Greenwich Observatory (UK), Gaming from One Place to Another , What Time Is It? grid partitioning, game space, Collision Detection ground plane, particle-to-ground collisions, Particle-to-Ground Collisions –Particle-to-Ground Collisions guns, shooting (see ballistics and firearms) gyroscopes, Sensing Orientation H Hamilton, William, Quaternions haptic feedback in touch screens, Haptic Feedback harmonic wave, What Is Sound? , Harmonic Wave Harr-like features (optical tracking), OpenCV haversine formula for distance, Distance head-related transfer functions (HRTFs), How We Hear in 3D heave motion in ships and boats, Ship Motions , Heave hectoPascals (hPa), Barometers heuristic subroutines, Passive Stereoization high lift devices, Lift and Drag high-pass filters (accelerometers), Accelerometers higher-order terms, Euler’s Method Hoerner, Sighard F., Lift and Drag , Other Forces holographs, Advanced Technologies Hooke’s law, Springs and Dampers , Springs and Dampers horsepower in cars, Power hovercraft about, Hovercraft –How Hovercraft Work aerodynamic drag on, Force Effectors , Resistance –Resistance implementing collision response, Implementing Collision Response –Angular Effects resistance in, Resistance –Resistance steering, How Hovercraft Work , Steering 2D rigid-body
simulation, 2D Rigid-Body Simulator –Tuning hPa (hectoPascals), Barometers HRTFs (head-related transfer functions), How We Hear in 3D hull in ships and boats, Ships and Boats hull speed, Guidance speeds human action modeling (see sports) hydrodynamic lift, Ships and Boats hydrostatic pressure, Pressure , Example Effects of High Pressure I impact billiard characteristics for, Billiards center of mass and, Impact central, Impact , Linear Collision Response collisions and, Impact –Impact conservation of momentum principle, Impact , Impact , Recoil and Impact direct, Impact direct central, Impact oblique, Impact improved Euler method, Better Methods –Better Methods impulse angular, Impulse-Momentum Principle , Linear and Angular Impulse –Linear and Angular Impulse , Friction defined, Impulse-Momentum Principle linear, Impulse-Momentum Principle , Linear and Angular Impulse –Linear and Angular Impulse , Linear Collision Response projectiles and, Projectiles impulse torque, Impulse-Momentum Principle impulse-momentum principle, Impulse-Momentum Principle , Collision Response indirect force effectors, Force Effectors induced drag, Resistance inelastic collisions, Impact inertia tensors about, Inertia Tensor angular momentum equation, Inertia Tensor calculating, Inertia Tensor , Model products of inertia, Inertia Tensor symmetry and, Inertia Tensor transfer of axis formula, Inertia Tensor inertia, defined, Steering infrared touch screens, Infrared and Optical Imaging initial value problem, Integrating the Equations of Motion instantaneous acceleration, Velocity and Acceleration instantaneous velocity calculating, Constant Acceleration defined, Velocity and Acceleration integral photography, Advanced Technologies integrals, defined, Derivatives and Integrals integrators 3D rigid-body simulation, Integration –Integration about, Particles numerical, Numerical Integrator particle simulation, Integrator 2D rigid-body
simulation, Integrator –Integrator intensity of sound, What Is Sound? interaural delay, How We Hear in 3D internal ballistics, Projectile Motion International System of Units (SI), Units and Measures International Towing Tank Conference (ITTC), General Resistance intraocular distance, Active Stereoization inverse, in matrix operations, Inverse isotropic materials, Newton’s Second Law of Motion ITTC ( International Towing Tank Conference), General Resistance K Kaehler, Adrian, OpenCV Kinect system, Kinect kinematic viscosity, Units and Measures kinematics about, Kinematics angular velocity and acceleration, Angular Velocity and Acceleration –Angular Velocity and Acceleration constant acceleration, Constant Acceleration –Constant Acceleration local coordinate axes, Local Coordinate Axes nonconstant acceleration, Nonconstant Acceleration particle explosion, Kinematic Particle Explosion –Kinematic Particle Explosion , Particle Explosions –Particle Explosions rigid-body, Rigid-Body Kinematics 3D particle, 3D Particle Kinematics –Hitting the Target 2D particle, 2D Particle Kinematics –2D Particle Kinematics velocity and acceleration, Velocity and Acceleration –Velocity and Acceleration kinetic energy about, Impact of bullets, Recoil and Impact , Particle Explosions –Particle Explosions converting, Impact of sound waves, What Is Sound? kinetic weapons, Recoil and Impact kinetics about, Kinetics –Kinetics problem-solving guidelines, Kinetics rigid-body, Rigid-Body Kinetics –Rigid-Body Kinetics 3D particle, Particle Kinetics in 3D –Cannon Revised 2D particle, Particle Kinetics in 2D –Particle Kinetics in 2D kneeling (shooting position), Breathing and Body Position Kutta condition, Lift and Drag Kutta-Joukouski theorem, Magnus Effect L laminar flow, Fluid Dynamic Drag latitude calculating distance between longitude and, Location, Location, Location –Rhumb Line defined, Gaming from One Place to Another trilateration technique and, Two-Dimensional Mathematical Treatment –Two-Dimensional Mathematical Treatment LC (liquid-crystal) shutter glasses, Liquid-Crystal Plasma LED technology, Infrared and Optical Imaging length of aircraft wings, Geometry of ships and boats, Ships and Boats units and symbols for, Units and Measures , Units and Measures lenticular lenses, Autostereoscopy lift force about, Magnus Effect –Magnus Effect aerostatic lift, How Hovercraft Work aircraft in flight and, Aircraft , Lift and Drag –Lift and Drag calculating, Magnus Effect lift-to-drag ratio, Lift and Drag light polarization of, Linear and Circular Polarization –Linear and Circular Polarization speed of, Relativistic Time –Relativistic Time , Two-Dimensional Mathematical Treatment linear acceleration in billiards example, Calculating Forces force and, Force and Torque Newton’s second law of motion and, Newton’s Laws of Motion , Newton’s Second Law of Motion units and symbols for, Units and Measures , Units and Measures linear collision response, Linear Collision Response –Linear Collision Response linear impulse in collisions, Linear and Angular Impulse –Linear and Angular Impulse , Linear Collision Response in impulse-momentum principle, Impulse-Momentum Principle linear kinetic energy, Impact linear momentum, Newton’s Second Law of Motion linear motion, Mass, Center of Mass, and Moment of Inertia linear polarization of light, Linear and Circular Polarization –Linear and Circular Polarization linear velocity equation for, Angular Velocity and Acceleration linked-chain example, Update units and symbols for, Units and Measures linked-chain example, Connecting Rigid Bodies –Rotational Restraint liquid-crystal (LC) shutter glasses, Liquid-Crystal Plasma liquid-crystal plasma displays, Liquid-Crystal Plasma load cells center of gravity and, Center of gravity –Center of gravity defined, Pressure Sensors and Load Cells gaming uses for, Pressure Sensors and Load Cells , Load Cells strain gauges and, Tiny scales local coordinate system, Local Coordinate Axes , Geometry locality principle, Relativistic Time location-based gaming about, Location-Based Gaming geographic coordinate system and, Gaming from One Place to Another longitude calculating distance between latitude and, Location, Location, Location –Rhumb Line defined, Gaming from One Place to Another origin of determining, What Time Is It? trilateration technique and, Two-Dimensional Mathematical Treatment –Two-Dimensional Mathematical Treatment longitudinal waves, Linear and Circular Polarization Lorentz factor, Relativistic Time Lorentz transformation, Relativistic Time –Relativistic Time loudness in sound, What Is Sound? low-pass filters (accelerometers), Accelerometers M magnitude in polygon explosions, Polygon Explosions in quaternion operations, Magnitude , Magnitude scalars and, Vectors tensors and, Newton’s Second Law of Motion of torque, Force and Torque in vector operations, Vectors , Magnitude of velocity, Velocity and Acceleration Magnus effect, Magnus Effect –Magnus Effect MakeEulerAnglesFromQ function, MakeEulerAnglesFromQ , Integration , MakeEulerAnglesFromQ MakeQFromEulerAngles function, MakeQFromEulerAngles , MakeQFromEulerAngles maneuverability of ships and boats, Maneuverability mass, Accelerometer Theory (see also center of mass) accelerometer theory on, Accelerometer Theory calculating, Mass, Center of Mass, and Moment of Inertia defined, Mass, Center of Mass, and Moment of Inertia Newton’s second law of motion and, Newton’s Laws of Motion , Newton’s Second Law of Motion 2D example, Mass, Center of Mass, and Moment of Inertia units and symbols for, Units and Measures , Units and Measures , Units and Measures variable, Variable Mass virtual, Virtual mass mass flow rate, Resistance mass moment of inertia calculating, Mass, Center of Mass, and Moment of Inertia –Mass, Center of Mass, and Moment of Inertia defined, Mass, Center of Mass, and Moment of Inertia physics models and, Physics Models 2D example, Mass, Center of Mass, and Moment of Inertia –Mass, Center of Mass, and Moment of Inertia units and symbols for, Units and Measures mass properties center of mass, Mass, Center of Mass, and Moment of Inertia , Mass, Center of Mass, and Moment of Inertia –Mass, Center of Mass, and Moment of Inertia defined, Mass, Center of Mass, and Moment of Inertia mass, Mass, Center of Mass, and Moment of Inertia , Mass, Center of Mass, and Moment of Inertia mass moment of inertia, Mass, Center of Mass, and Moment of Inertia , Mass, Center of Mass, and Moment of Inertia –Mass, Center of Mass, and Moment of Inertia 2D example, Mass, Center of Mass, and Moment of Inertia –Mass, Center of Mass, and Moment of Inertia matrix addition, Matrix Addition: The += Operator , Matrix Addition: The + Operator matrix functions and operators matrix addition, Matrix Addition: The += Operator , Matrix Addition: The + Operator matrix multiplication, Matrix Multiplication: The * Operator matrix subtraction, Matrix Subtraction: The −= Operator , Matrix Subtraction: The − Operator scalar division, Scalar Division: The /= Operator , Scalar Divide: The / Operator scalar multiplication, Scalar Multiplication: The *= Operator , Scalar Multiplication: The * Operator vector multiplication, Vector Multiplication: The * Operator matrix multiplication, Matrix Multiplication: The * Operator matrix operations matrix functions and operators, Matrix Functions and Operators –Vector Multiplication: The * Operator Matrix3x3 class, Matrix3×3 Class –Scalar Division: The /= Operator matrix subtraction, Matrix Subtraction: The −= Operator , Matrix Subtraction: The − Operator Matrix3x3 class about, Matrix3×3 Class det method, Determinant Inverse method, Inverse matrix addition, Matrix Addition: The += Operator matrix subtraction, Matrix Subtraction: The −= Operator scalar division, Scalar Division: The /= Operator scalar multiplication, Scalar Multiplication: The *= Operator Transpose method, Transpose mean camber line, Geometry measures (see units and measures) MEMS (microelectromechanical systems), Accelerometers –MEMS Accelerometers , Barometers Mercator projection, Rhumb Line metacenter, in ship stability, Stability microelectromechanical systems (MEMS), Accelerometers –MEMS Accelerometers , Barometers mixed-reality games, Mixed Reality Miyamoto, Shigeru, Load Cells models 3D rigid-body simulation, Model –Model about, Particles aircraft flight, Modeling –Modeling connecting objects examples, Connecting Objects –Rotational Restraint particle simulation, Simple Particle Model –Simple Particle Model physics, Physics Models 2D rigid-body
simulation, Model modulo operator, Great-Circle Heading moment (see torque) moment of inertia calculating, Mass, Center of Mass, and Moment of Inertia –Mass, Center of Mass, and Moment of Inertia , Inertia Tensor , Model defined, Mass, Center of Mass, and Moment of Inertia laws of motion and, Newton’s Second Law of Motion rigid-body kinetics and, Rigid-Body Kinetics 3D example, Newton’s Second Law of Motion 2D example, Mass, Center of Mass, and Moment of Inertia –Mass, Center of Mass, and Moment of Inertia momentum angular, Newton’s Second Law of Motion , Inertia Tensor conservation of momentum principle, Impact , Impact , Recoil and Impact linear, Newton’s Second Law of Motion momentum drag, Resistance motion angular, Mass, Center of Mass, and Moment of Inertia , Rigid-Body Kinetics –Rigid-Body Kinetics , Particle Explosions coupled, Ship Motions , Coupled Motions linear, Mass, Center of Mass, and Moment of Inertia plane, Rigid-Body Kinematics projectile, Projectile Motion –Projectile Motion ship, Ship Motions –Coupled Motions motion-identifying condition table, Center of gravity mouse-based input versus touch screens, Difference from Mouse-Based Input movement parallax, Binocular Vision multiplication (*) operator in matrix operations, Matrix Multiplication: The * Operator , Scalar Multiplication: The * Operator , Vector Multiplication: The * Operator in quaternion operations, Quaternion multiplication: The * operator , Vector multiplication: The * operator , Quaternion Multiplication: The * Operator , Scalar Multiplication: The * Operator , Vector Multiplication: The * Operator in vector operations, Vector Dot Product: The * Operator , Scalar Multiplication: The * Operator multiplication (*=) operator in matrix operations, Scalar Multiplication: The *= Operator in quaternion operations, Scalar Multiplication: The *= Operator in vector operations, Scalar Multiplication: The *= Operator muzzle velocity, Projectile Motion N NACA foil sections, Lift and Drag neutral axis, Mass, Center of Mass, and Moment of Inertia Newton, Isaac, Newton’s Laws of Motion Newton’s laws conservation of momentum principle, Impact , Impact , Recoil and Impact equal and opposite forces, Springs and Dampers , Numerical Integrator equations of motion and, Kinetics , Particle Kinetics in 2D Impulse-Momentum Principle and, Impulse-Momentum Principle of motion, Accelerometer Theory of gravitation, Force Fields of motion, Newton’s Laws of Motion , Units and Measures , Newton’s Second Law of Motion –Newton’s Second Law of Motion , Forces , Force Fields nonconstant acceleration, Nonconstant Acceleration normalize, in vector operations, Normalize numerical integrators, Numerical Integrator O object detection (optical tracking), OpenCV Objective-C accelerometer code example, Two Degrees of Freedom –Two Degrees of Freedom calculating distances code example, Distance , Rhumb Line objects aggregating forces, Numerical Integrator collision detection considerations, Collision Detection connecting, Connecting Objects –Rotational Restraint jittering problem, Collision Response simulated objects manager for, Simulated Objects Manager weight of, Units and Measures , Stability , Projectile Motion oblique impact, Impact occlusion in volumetric displays, Advanced Technologies off-axis method (cameras), The Left and Right Frustums opacity (alpha), Optical Tracking OpenAL API about, Sound alDistanceModel function, Attenuation alSpeedOfSound function, Speed of Sound AL_SPEED_OF_SOUND property, Speed of Sound Doppler effect, Doppler Effect reverberation special effect, Reflection 3D sound example, A Simple Example –A Simple Example OpenCV method for 3D reconstruction, OpenCV optical sensors and tracking about, Optical Tracking , Sensors and SDKs Kinect system, Kinect numerical differentiation, Numerical Differentiation –Numerical Differentiation OpenCV method for 3D reconstruction, OpenCV optimal imaging techniques, Infrared and Optical Imaging orientation computing in 2D rigid-body simulation, Model , Integrator defining in cannon ball game example, X Components expressing in 3D rigid-body simulations, Rotation in 3D Rigid-Body Simulators , Rotation Matrices importance in rigid bodies, Kinematics quaternions and, Quaternions , Quaternions in 3D Simulators –Quaternions in 3D Simulators , Model , Integration sensing with accelerometers, Simple Particle Model , Sensing Orientation tracking during body rotation, Local Coordinate Axes out-of-screen effects, Active Stereoization overshoot angle, Rudders and Thrust Vectoring oversteering cars, Steering P parallax, Binocular Vision parallax barrier in autostereoscopy, Autostereoscopy parallel axis theorem, Mass, Center of Mass, and Moment of Inertia , Mass, Center of Mass, and Moment of Inertia parameter tuning, Projectiles particle explosions, Kinematic Particle Explosion –Kinematic Particle Explosion , Particle Explosions –Particle Explosions particle kinematics particle explosions, Kinematic Particle Explosion –Kinematic Particle Explosion , Particle Explosions –Particle Explosions 3D, 3D Particle Kinematics –Hitting the Target 2D, 2D Particle Kinematics –2D Particle Kinematics particle kinetics 3D, Particle Kinetics in 3D –Cannon Revised 2D, Particle Kinetics in 2D –Particle Kinetics in 2D particle simulation about, Particles –Particles basic simulator, The Basic Simulator –The Basic Simulator implementing collisions, Implementing Collisions –Particle-to-Obstacle Collisions implementing external forces, Implementing External Forces –Implementing External Forces integrating particles, Integrator rendering particles, Rendering simple model, Simple Particle Model –Simple Particle Model tuning, Tuning particle-to-ground collisions, Particle-to-Ground Collisions –Particle-to-Ground Collisions particle-to-obstacle collisions, Particle-to-Obstacle Collisions –Particle-to-Obstacle Collisions particles about, Kinematics cloth simulation, Connecting Objects connecting, Connecting Particles –Update the simulation hanging rope or vine example, Connecting Particles –Update the simulation integrating in simulator, Integrator rendering in simulator, Rendering uses for, Particles passive stereoization, Programming Considerations , Passive Stereoization pattern recognition, Optical Tracking penalty methods, Collisions penetration in collisions, Linear Collision Response , Linear Collision Response , Collision Response percussion, center of, Impact photodetectors, Infrared and Optical Imaging photons, defined, Relativistic Time physics engines about, Physics Engines building, Building Your Own Physics Engine –Building Your Own Physics Engine collision detection in, Building Your Own Physics Engine , Collision Detection collision response in, Building Your Own Physics Engine , Collision Response force effectors and, Force Effectors general-purpose, Building Your Own Physics Engine numerical integrators and, Numerical Integrator physics models, Physics Models purpose-built, Building Your Own Physics Engine simulated objects manager, Simulated Objects Manager physics models, Physics Models piezoresisters, MEMS Accelerometers , Barometers piezoresistive strain gauge, Tiny scales pinned joint, Rotational Restraint pitch flight control action for, Rotation in 3D Rigid-Body Simulators , Flight Controls , Flight Controls , Control local coordinate axes and, Local Coordinate Axes , Geometry quarter-chord point and, Lift and Drag , Control in ships and boats, Stability , Ship Motions , Pitch in sound, What Is Sound? plane motion, Rigid-Body Kinematics planing vessels, Ships and Boats , Planing craft plastic collisions, Impact plenum chamber (hovercraft), How Hovercraft Work point sound source, Attenuation point-blank weapons, Taking Aim polarization of light, Linear and Circular Polarization –Linear and Circular Polarization polling rate, Accelerometers polygon explosions, Polygon Explosions –Polygon Explosions pounds per square foot (psf), Pressure pounds per square inch (psi), Pressure power of car engines, Power defined, Power hovercraft hover height and, How Hovercraft Work of sound wave, What Is Sound? pressure atmospheric, Under Pressure , Barometers Bernoulli’s equation and, Drag , Lift and Drag buoyancy and, Buoyancy center of, Force Effectors defined, Under Pressure force versus, Pressure hydrostatic, Pressure , Example Effects of High Pressure sound and, What Is Sound? units and symbols for, Units and Measures , Under Pressure pressure drag, General Resistance , Resistance pressure sensors about, Pressure Sensors and Load Cells –Example Effects of High Pressure load cells and, Load Cells –Center of gravity pressure-sensitive buttons and, Button Mashing –Button Mashing principal axes, Inertia Tensor products of inertia, Inertia Tensor projectiles about, Projectiles –Projectiles bullets in motion, Projectile Motion –Projectile Motion drag and, Drag –Drag football simulation game, Kinematic Particle Explosion golf ball flight, Modeling a Golf Swing hitting the target example, Hitting the Target –Hitting the Target impulse forces, Impulse-Momentum Principle Magnus effect, Magnus Effect –Magnus Effect particle explosions as, Kinematic Particle Explosion –Kinematic Particle Explosion , Particle Explosions –Particle Explosions recoil and impact, Recoil and Impact simple trajectories, Simple Trajectories –Simple Trajectories taking aim, Taking Aim –Breathing and Body Position terminal velocity and, Drag variable mass and, Variable Mass prone (shooting position), Breathing and Body Position propeller walk, Propeller walk propulsion of ships and boats, Propulsion pseudoranges, Two-Dimensional Mathematical Treatment psf (pounds per square foot), Pressure psi (pounds per square inch), Pressure Q QGetAngle function, QGetAngle QGetAxis function, QGetAxis QRotate function, QRotate quantum tunneling, Common Accelerometer Specifications quarter-chord point, Lift and Drag , Control quaternion addition, Quaternion Addition: The += Operator , Quaternion Addition: The + Operator Quaternion class about, Quaternion Operations , Quaternion Class conjugate operator, Conjugate: The ~ operator , Conjugate: The ~ Operator GetScalar method, GetScalar GetVector method, GetVector Magnitude method, Magnitude , Magnitude quaternion addition, Quaternion Addition: The += Operator quaternion subtraction, Quaternion Subtraction: The −= Operator scalar division, Scalar Division: The /= Operator scalar multiplication, Scalar Multiplication: The *= Operator quaternion functions and operators conjugate operator, Conjugate: The ~ operator , Conjugate: The ~ Operator conversion functions, Conversion Functions DegreesToRadians function, Conversion Functions MakeEulerAnglesFromQ function, MakeEulerAnglesFromQ , Integration , MakeEulerAnglesFromQ MakeQFromEulerAngles function, MakeQFromEulerAngles , MakeQFromEulerAngles QGetAngle function, QGetAngle QGetAxis function, QGetAxis QRotate function, QRotate quaternion addition, Quaternion Addition: The += Operator , Quaternion Addition: The + Operator quaternion multiplication, Quaternion multiplication: The * operator , Quaternion Multiplication: The * Operator quaternion subtraction, Quaternion Subtraction: The −= Operator , Quaternion Subtraction: The − Operator QVRotate function, QVRotate , Quaternions in 3D Simulators , Model , QVRotate RadiansToDegrees function, Conversion Functions scalar division, Scalar Division: The /= Operator , Scalar Division: The / Operator scalar multiplication, Scalar Multiplication: The *= Operator , Scalar Multiplication: The * Operator vector multiplication, Vector multiplication: The * operator , Vector Multiplication: The * Operator quaternion multiplication, Quaternion multiplication: The * operator , Quaternion Multiplication: The * Operator quaternion operations Quaternion class, Quaternion Operations , Quaternion Class –Conjugate: The ~ Operator quaternion functions and operators, Quaternion Functions and Operators –Conversion Functions for rigid-body rotation, Quaternions –MakeEulerAnglesFromQ 3D simulation and, Quaternions in 3D Simulators –Quaternions in 3D Simulators quaternion subtraction, Quaternion Subtraction: The −= Operator , Quaternion Subtraction: The − Operator QVRotate function, QVRotate , Quaternions in 3D Simulators , Model , QVRotate R RadiansToDegrees function, Conversion Functions rarefaction, What Is Sound? real-time simulations about, Real-Time Simulations equations of motion and, Integrating the Equations of Motion –Integrating the Equations of Motion Euler’s method, Euler’s Method –Euler’s Method improved Euler method, Better Methods –Better Methods physics engine considerations, Building Your Own Physics Engine Runge-Kutta method in, Better Methods –Better Methods Taylor’s theorem in, Euler’s Method , Better Methods recoil of firearms, Recoil and Impact rectangular cylinder, mass moment of inertia formula, Mass, Center of Mass, and Moment of Inertia reflection in sound waves, Reflection relative acceleration, Angular Velocity and Acceleration relative normal velocity, Linear Collision Response relative velocity about, Angular Velocity and Acceleration between connected objects, Springs and Dampers collision detection and, Linear Collision Response , Linear Collision Response , Collision Detection particle-to-ground collisions and, Particle-to-Ground Collisions relativistic time, Relativistic Time –Relativistic Time , Two-Dimensional Mathematical Treatment rendering about, Particles particle simulation, Rendering simulated objects manager and, Simulated Objects Manager 2D rigid-body
simulation, Rendering residual resistance, General Resistance resistance in cars, Resistance equation for, Particle Kinetics in 2D in hovercraft, Resistance –Resistance residual, General Resistance rolling, Resistance , Calculating Forces in ships and boats, General Resistance –Guidance speeds zeroing the sights and, Bullet drop: Gravity and air resistance –Bullet drop: Gravity and air resistance resistive touch screens, Resistive , Resistive Touch Screens –Four-wire resistive touch screen restitution, coefficient of (see coefficient of restitution) reverberation special effect, Reflection reverse geocaching, Geocaching and Reverse Geocaching reverse, in vector operations, Reverse Reynolds number, Drag , General Resistance rhumb line, Location, Location, Location , Rhumb Line right hand rule, Force and Torque rigid bodies about, Kinematics billiards example, Implementation circular path of particles making up, Angular Velocity and Acceleration connecting, Connecting Rigid Bodies –Rotational Restraint conservation of momentum principle, Impact , Impact , Recoil and Impact linked-chain example, Connecting Rigid Bodies –Rotational Restraint penalty methods for, Collisions rotation in 3D simulation, Rotation in 3D Rigid-Body Simulators –Quaternions in 3D Simulators 3D simulation for, 3D Rigid-Body Simulator –Flight Controls , Implementation 2D simulation for, 2D Rigid-Body Simulator –Tuning rigid-body kinematics, Rigid-Body Kinematics rigid-body kinetics, Rigid-Body Kinetics –Rigid-Body Kinetics roadway bank, Steering Robbins effect, Magnus Effect –Magnus Effect roll flight control action for, Rotation in 3D Rigid-Body Simulators , Flight Controls local coordinate axes and, Local Coordinate Axes , Geometry in ships and boats, Stability , Ship Motions , Roll roll period, Roll rolling resistance, Resistance , Calculating Forces rope example, Connecting Particles –Update the simulation rotation in 3D rigid-body simulation about, Rotation in 3D Rigid-Body Simulators quaternions and, Quaternions –Quaternions in 3D Simulators rotation matrices and, Rotation Matrices –Rotation Matrices rotational restraint, Rotational Restraint –Rotational Restraint rotation matrices, Rotation Matrices –Rotation Matrices rotational acceleration, Force and Torque rotational inertia (see mass moment of inertia) rotational restraint, Rotational Restraint –Rotational Restraint rudders in aircraft, Geometry , Control in ships and boats, Rudders and Thrust Vectoring Runge-Kutta method, Better Methods –Better Methods , Modeling a Golf Swing , Solving the Golf Swing Equations S Saffer, Dan, Custom Gestures scalar division in matrix operations, Scalar Division: The /= Operator , Scalar Divide: The / Operator in quaternion operations, Scalar Division: The /= Operator , Scalar Division: The / Operator in vector operations, Scalar Division: The /= Operator , Scalar Division: The / Operator scalar multiplication in matrix operations, Scalar Multiplication: The *= Operator , Scalar Multiplication: The * Operator in quaternion operations, Scalar Multiplication: The *= Operator , Scalar Multiplication: The * Operator in vector operations, Scalar Multiplication: The *= Operator , Scalar Multiplication: The * Operator , Triple Scalar Product scalars defined, Vectors examples of, Vectors magnitude and, Vectors tensors and, Newton’s Second Law of Motion second derivatives, Velocity and Acceleration second zero, Bullet drop: Gravity and air resistance second-order central difference, Numerical Differentiation separation point in fluid dynamic drag, Drag ships and boats about, Ships and Boats –Ships and Boats geometry of, Ships and Boats maneuverability of, Maneuverability –Propeller walk parts of, Ships and Boats propulsion of, Propulsion resistance in, General Resistance –Guidance speeds ship motions, Ship Motions –Coupled Motions sinking, Sinking stability of, Stability –Stability 2D particle
kinetics example, Particle Kinetics in 2D –Particle Kinetics in 2D types of, Ships and Boats typical speeds for, Guidance speeds shooting guns example air drag and, Drag challenges of, Projectile Motion particle kinematics suggestions, Kinematic Particle Explosion physics engine considerations, Building Your Own Physics Engine taking aim, Taking Aim 3D particle
kinematics, 3D Particle Kinematics –Hitting the Target 3D particle
kinetics, Particle Kinetics in 3D –Cannon Revised 2D particle
kinematics, 2D Particle Kinematics –2D Particle Kinematics shooting positions, Breathing and Body Position SI (International System of Units), Units and Measures simulated objects manager, Simulated Objects Manager simulations cloth, Connecting Objects football game, Kinematic Particle Explosion force effectors in, Force Effectors hitting the target example, Hitting the Target –Hitting the Target implementing collision response, Implementing Collision Response –Angular Effects particle, Particles –Tuning physics engine considerations, Building Your Own Physics Engine real-time, Real-Time Simulations –Summary , Building Your Own Physics Engine springs and dampers in, Springs and Dampers 3D rigid-body, Rotation in 3D Rigid-Body Simulators –Quaternions in 3D Simulators , 3D Rigid-Body Simulator –Flight Controls 2D rigid-body, 2D Rigid-Body Simulator –Tuning updating, Update the simulation –Update the simulation , Update –Update sinking ships and boats, Sinking skidding distance, Stopping Distance skin friction on aircraft, Other Forces on cars, Resistance on hovercraft, Resistance planing vessels and, Planing craft sliding friction force, Calculating Forces sound and sound waves about, Sound –What Is Sound? characteristics of, Characteristics of and Behavior of Sound Waves –Doppler Effect 3D, 3D Sound –A Simple Example span, aircraft wings, Geometry special effects fade effect, Kinematic Particle Explosion out-of-screen effects, Active Stereoization particle explosions, Kinematic Particle Explosion reverberation, Reflection specific weight, Buoyancy speed acceleration and, Velocity and Acceleration calculating, Velocity and Acceleration defined, Velocity and Acceleration drag and, Drag equations of motion and, Particle Kinetics in 2D hull, Guidance speeds of light, Relativistic Time –Relativistic Time , Two-Dimensional Mathematical Treatment of sound, Speed of Sound units and symbols for, Units and Measures , Velocity and Acceleration velocity and, Velocity and Acceleration spheres bounding, Collision Detection calculating distance along, Distance fluid dynamic drag around, Drag –Drag great-circle heading, Great-Circle Heading Magnus effect and, Magnus Effect mass moment of inertia formula, Mass, Center of Mass, and Moment of Inertia spherical law of cosines, Distance spherical shell, mass moment of inertia formula, Mass, Center of Mass, and Moment of Inertia sports about, Sports baseball examples, Impact –Impact , Magnus Effect billiards examples, Impact –Impact , Billiards –Handling Collisions football game simulation, Kinematic Particle Explosion golf examples, Friction –Friction , Magnus Effect , Building Your Own Physics Engine , Modeling a Golf Swing –Solving the Golf Swing Equations spring-damper element formula, Springs and Dampers , Connecting Objects , Springs and Dampers springs about, Springs and Dampers accelerometer theory on, Accelerometer Theory cloth simulation, Connecting Objects connecting objects, Springs and Dampers equation for, Springs and Dampers , Springs and Dampers swinging rope example, Rope –Update the simulation uses for, Springs and Dampers stability index (GM), Stability stability of ships and boats, Stability –Stability standing (shooting position), Breathing and Body Position static forces, Friction steering in cars, Steering –Steering in hovercraft, How Hovercraft Work , Steering throttle, Rudders and Thrust Vectoring Stein, Jonathan Y., Accelerometers stereoization process about, Programming Considerations active stereoization, Programming Considerations –Active Stereoization passive stereoization, Programming Considerations , Passive Stereoization stereopsis, Binocular Vision stereoscopic displays, 3D Display (see also 3D display) about, 3D Display , Stereoscopic Basics viewing frustum, The Left and Right Frustums –The Left and Right Frustums stopping distance in cars, Stopping Distance strain energy, Impact strain gauges, Tiny scales street games, Street Games subtraction (−) operator in matrix operations, Matrix Subtraction: The − Operator in quaternion operations, Quaternion Subtraction: The − Operator in vector operations, Vector Subtraction: The − Operator subtraction (−=) operator in matrix operations, Matrix Subtraction: The −= Operator in quaternion operations, Quaternion Subtraction: The −= Operator in vector operations, Vector Subtraction: The −= Operator summation in binocular vision, Binocular Vision superelevation (roadway banking), Steering superposition principle, Superposition suppression in binocular vision, Binocular Vision surface acoustic wave technology, Exotic: Dispersive Signal and Surface Acoustic Wave surface area, units and symbols for, Units and Measures symmetry, plane of, Inertia Tensor T tangential acceleration, Angular Velocity and Acceleration tangential velocity, Angular Velocity and Acceleration , Impact Taylor’s theorem, Euler’s Method , Better Methods tensors about, Newton’s Second Law of Motion inertia, Inertia Tensor –Inertia Tensor , Model scalars and, Newton’s Second Law of Motion vectors and, Newton’s Second Law of Motion 10/10 maneuver, Rudders and Thrust Vectoring terminal ballistics, Projectile Motion terminal velocity, Drag 3D display about, 3D Display binocular vision, Binocular Vision –Binocular Vision programming considerations, Programming Considerations –Passive Stereoization stereoscopic basics, Stereoscopic Basics –The Left and Right Frustums types of, Types of Display –Advanced Technologies 3D particle
kinematics about, 3D Particle Kinematics hitting the target, Hitting the Target –Hitting the Target shooting guns example, 3D Particle Kinematics –Hitting the Target vectors, The Vectors x components, X Components –X Components y components, Y Components z components, Z Components 3D particle
kinetics about, Particle Kinetics in 3D –Particle Kinetics in 3D shooting guns example, Particle Kinetics in 3D –Cannon Revised x components, X Components y components, Y Components z components, Z Components 3D rigid-body simulation about, 3D Rigid-Body Simulator billiard ball example, Implementation flight controls, Flight Controls –Flight Controls , Modeling –Modeling integrator for, Integration –Integration model for, Model –Model quaternions in, Quaternions in 3D Simulators –Quaternions in 3D Simulators rotation in, Rotation in 3D Rigid-Body Simulators –Quaternions in 3D Simulators 3D sound, 3D Sound –A Simple Example throttle steering, Rudders and Thrust Vectoring thrust defined, Forces , Other Forces flight control actions, Flight Controls , Aircraft thrust vectoring, Rudders and Thrust Vectoring thrust-to-propeller RPM ratio, Propulsion thrust-to-throttle curve ratio, Propulsion thrust-to-weight ratio, Other Forces tilt controlling sprite with, Using Tilt to Control a Sprite –Two Degrees of Freedom sensing with accelerometers, Sensing Tilt time equations of motion and, Particle Kinetics in 2D GPS background and, What Time Is It? –Two-Dimensional Mathematical Treatment laws of motion and, Newton’s Second Law of Motion relativistic, Relativistic Time –Relativistic Time reliativistic, Two-Dimensional Mathematical Treatment speed and, Velocity and Acceleration tracking button position over, Button Mashing units and symbols for, Units and Measures , Units and Measures TNT equivalency, Polygon Explosions toe-in method (cameras), The Left and Right Frustums tons per centimeter immersion (TPCM), Heave torque about, Force and Torque calculating, Force and Torque force versus, Force and Torque –Force and Torque impulse, Impulse-Momentum Principle laws of motion and, Newton’s Second Law of Motion magnitude of, Force and Torque rotational acceleration and, Force and Torque units and symbols for, Units and Measures touch screens about, Touch Screens custom gestures and, Custom Gestures example program, Example Program –Multitouch haptic feedback, Haptic Feedback modeling in games, Modeling Touch Screens in Games mouse-based input versus, Difference from Mouse-Based Input step-by-step physics, Resistive Touch Screens –Mutual capacitance types of, Resistive TPCM (tons per centimeter immersion), Heave trajectories football simulation game, Kinematic Particle Explosion hitting the target example, Hitting the Target –Hitting the Target simple, Simple Trajectories –Simple Trajectories terminal velocity and, Drag zeroing the sights, Zeroing the Sights –Wind transfer functions (sound), How We Hear in 3D transfer of axis formula, Inertia Tensor transforming coordinates, 2D rigid-body
simulation, Transforming Coordinates transitional ballistics, Projectile Motion transpose, in matrix operations, Transpose transverse waves, Linear and Circular Polarization trilateration technique, Two-Dimensional Mathematical Treatment –Two-Dimensional Mathematical Treatment triple scalar product, Triple Scalar Product triple vector product, Inertia Tensor truncation error, Euler’s Method –Euler’s Method tuning particle simulation, Tuning 2D rigid-body
simulation, Tuning turbulent flow, Fluid Dynamic Drag turbulent wake, Drag two-rod model, Modeling a Golf Swing 2D particle
kinematics, 2D Particle Kinematics –2D Particle Kinematics 2D particle
kinetics, Particle Kinetics in 2D –Particle Kinetics in 2D 2D rigid-body
simulation about, 2D Rigid-Body Simulator basic simulator, The Basic Simulator –The Basic Simulator implementing collision response, Implementing Collision Response –Angular Effects integrator for, Integrator –Integrator model for, Model –Model rendering, Rendering tuning, Tuning U understeering cars, Steering uniform density, Rigid-Body Kinetics unit quaternion, Quaternions , Quaternions in 3D Simulators , Integration units and measures checking dimensional consistency, Units and Measures –Units and Measures common mistakes when calculating, Units and Measures for pressure, Pressure , Under Pressure for sound, What Is Sound? universal constant, Force Fields V variable mass, Variable Mass vector addition, Vector Addition: The += Operator , Vector Addition: The + Operator Vector class about, Vector Class conjugate operator, Conjugate: The − Operator Magnitude method, Magnitude Normalize method, Normalize in particle simulation, Simple Particle Model Reverse method, Reverse scalar division and, Scalar Division: The /= Operator scalar multiplication and, Scalar Multiplication: The *= Operator vector addition and, Vector Addition: The += Operator vector subtraction and, Vector Subtraction: The −= Operator vector cross product, Vectors , Angular Velocity and Acceleration , Vector Cross Product: The ^ Operator vector direction cosines, X Components , Magnitude vector dot-product operator, Vectors , Vector Dot Product: The * Operator vector functions and operators conjugate operator, Conjugate: The − Operator scalar division, Scalar Division: The /= Operator , Scalar Division: The / Operator scalar multiplication, Scalar Multiplication: The *= Operator , Scalar Multiplication: The * Operator triple scalar product, Triple Scalar Product vector addition, Vector Addition: The += Operator , Vector Addition: The + Operator vector cross product, Vectors , Angular Velocity and Acceleration , Vector Cross Product: The ^ Operator vector dot product, Vectors , Vector Dot Product: The * Operator vector subtraction, Vector Subtraction: The −= Operator , Vector Subtraction: The − Operator vector multiplication in matrix operations, Vector Multiplication: The * Operator in quaternion operations, Vector multiplication: The * operator , Vector Multiplication: The * Operator vector operations direction in, Vectors magnitude in, Vectors , Magnitude Vector class, Vector Class –Conjugate: The − Operator vector functions and operators, Vector Functions and Operators –Triple Scalar Product vector subtraction, Vector Subtraction: The −= Operator , Vector Subtraction: The − Operator vectors acceleration, Newton’s Second Law of Motion , Numerical Differentiation defined, Vectors examples of, Vectors orthogonal, Rotation Matrices tensors and, Newton’s Second Law of Motion 3D particle
kinematics and, The Vectors time derivative of, Newton’s Second Law of Motion velocity about, Velocity and Acceleration –Velocity and Acceleration acceleration and, Velocity and Acceleration –Velocity and Acceleration angular, Units and Measures , Newton’s Second Law of Motion , Angular Velocity and Acceleration –Angular Velocity and Acceleration , Rotation Matrices , Quaternions , Integration Bernoulli’s equation and, Drag equations for, Particle Kinetics in 2D instantaneous, Velocity and Acceleration , Constant Acceleration linear, Units and Measures , Angular Velocity and Acceleration , Update magnitude of, Velocity and Acceleration muzzle, Projectile Motion relative, Angular Velocity and Acceleration , Particle-to-Ground Collisions , Linear Collision Response , Linear Collision Response , Springs and Dampers , Collision Detection Reynolds number and, Drag second derivatives of, Velocity and Acceleration tangential, Angular Velocity and Acceleration , Impact terminal, Drag vertex-edge collisions, Angular Effects –Angular Effects vertex-vertex collisions, Angular Effects –Angular Effects vertical force, Calculating Forces vibration energy, Exotic: Dispersive Signal and Surface Acoustic Wave viewing frustum, The Left and Right Frustums –The Left and Right Frustums Vincenty formula, Distance vines (swinging) example, Connecting Particles –Update the simulation virtual mass, Virtual mass viscosity kinematic, Units and Measures units and symbols for, Units and Measures viscous drag, Resistance volume of ships, displacement and, Stability volumetric displays, 3D Display , Advanced Technologies Von Doenhoff, Albert E., Lift and Drag voxels, Advanced Technologies W wave drag, General Resistance , Resistance weather helm, Resistance weight of objects about, Units and Measures ammunition, Projectile Motion buoyancy and, Stability weighted average, Center of gravity –Center of gravity wetted drag, Resistance –Resistance wind force as force effector, Force Effectors particle kinetics in 3D, Particle Kinetics in 3D in particle simulation, Implementing External Forces –Implementing External Forces zeroing the sights and, Wind wings, in aircraft, Geometry wire-grid polarizer, Linear and Circular Polarization
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