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by Georges Vénizélos, Michel Borel
Movement Equations 3
Cover
Title
Copyright
Introduction
Table of Notations
1 Fundamental Principle of Dynamics
1.1. The fundamental principle of dynamics and its scalar consequences
1.2. Secondary principles
1.3. Motion of a set in a given frame λ
1.4. Motion of a non-deformable solid in a given frame
2 Solid in Space. Efforts and Links: Power
2.1. Degrees of freedom of a solid
2.2. Free solid
2.3. Linked solids and links
2.4. Virtual power developed on a material set
2.5. Power of the efforts exerted on a solid
2.6. Properties of power
3 Scalar Consequences and Movement Equations
3.1. Establishment principle of the movement equations
3.2. Movement equations of a solid
3.3. Movement equations of the free solid
3.4. Movement equations of the linked solid with configurable links
3.5. Energetic expression of the equations of analytical mechanics
3.6. Summary example
4 Particular Applications
4.1. Simulation of the motion of Earth
4.2. Foucault’s pendulum
5 Methodological Formulary
5.1. Reference outline on the motion of a solid
5.2. Kinematics of the solid
5.3. Principle of motion with fixed plane
5.4. Combination of motions
5.5. Kinetics of non-deformable solids
Bibliography
Index
End User License Agreement
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Title
Table of Contents
Cover
Title
Copyright
Introduction
Table of Notations
1 Fundamental Principle of Dynamics
1.1. The fundamental principle of dynamics and its scalar consequences
1.2. Secondary principles
1.3. Motion of a set
in a given frame
λ
1.4. Motion of a non-deformable solid in a given frame
2 Solid in Space. Efforts and Links: Power
2.1. Degrees of freedom of a solid
2.2. Free solid
2.3. Linked solids and links
2.4. Virtual power developed on a material set
2.5. Power of the efforts exerted on a solid
2.6. Properties of power
3 Scalar Consequences and Movement Equations
3.1. Establishment principle of the movement equations
3.2. Movement equations of a solid
3.3. Movement equations of the free solid
3.4. Movement equations of the linked solid with configurable links
3.5. Energetic expression of the equations of analytical mechanics
3.6. Summary example
4 Particular Applications
4.1. Simulation of the motion of Earth
4.2. Foucault’s pendulum
5 Methodological Formulary
5.1. Reference outline on the motion of a solid
5.2. Kinematics of the solid
5.3. Principle of motion with fixed plane
5.4. Combination of motions
5.5. Kinetics of non-deformable solids
Bibliography
Index
End User License Agreement
List of Illustrations
1 Fundamental Principle of Dynamics
Figure 1.1.
Set
in the universe
Figure 1.2.
The solar Galilean frame
Figure 1.3.
Relative position of the two frames
λ
and
μ
2 Solid in Space. Efforts and Links: Power
Figure 2.1.
Material set
Figure 2.2.
System of two opposing forces
3 Scalar Consequences and Movement Equations
Figure 3.1.
Exercise 1 – Situation of the system
Figure 3.2.
Exercise 1 – Situation of the system
Figure 3.3.
Exercise 1 – Representing points alignment
Figure 3.4.
Exercise 2 – Configuration of the solid
Figure 3.5.
Exercise 2 – Position of the center of rotation
Figure 3.6.
Exercise 3 – Orthogonal section of cylinder S
1
Figure 3.7.
Exercise 3 – Frame-solid set 1
Figure 3.8.
Exercise 3 – Angular parameters
Figure 3.9.
Configuration of the device
4 Particular Applications
Figure 4.1.
Spherical model of Earth
Figure 4.2.
Configuration of the rotation rate
Figure 4.3.
Diagrams of Euler’s representation
Figure 4.4.
Configurations of the rotation rate
Figure 4.5.
Model of Earth
Figure 4.6.
Trajectory of G
T
in the ecliptic plane
Figure 4.7.
Principle of Foucault’s pendulum
Figure 4.8.
Relative situation of the different frames
Figure 4.9.
Situation of the body in the new reference frame
Figure 4.10.
Identification of the point I
Figure 4.11.
Situation of Foucault’s pendulum
Figure 4.12.
Hypocycloidal trajectory of the point P
5 Methodological Formulary
Figure 5.1.
Principle of the Maxwell corkscrew
Figure 5.2.
Locating principle of a solid
Figure 5.3.
Cartesian coordinates
Figure 5.4.
Cylindro-polar coordinates
Figure 5.5.
Polar parameter
Figure 5.6.
Spherical coordinates
Figure 5.7.
Euler angles
Figure 5.8.
Situation of a solid onto the plane
Figure 5.9.
Trajectory of a material point
Figure 5.10.
Principle of plane motion on a plane
Figure 5.11.
Relative situation of two frames
Guide
Cover
Table of Contents
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