Linear multibody systems are the most popular dynamics model encountered in the field of engineering areas such as weaponry, robotics, aeronautics, astronautics, and machinery, etc. Research and engineering technicians are concerned with common dynamic problems related to linear multibody systems that mainly include eigenvalue problems, vibration characteristics, steady state response of the system, orthogonality of the eigenvectors, and the solution of the dynamics response, etc. The transfer matrix method for linear multibody systems (LMSTMM) is developed in this part, the concepts of body dynamics equations, augmented eigenvectors, and augmented operators proposed by the authors are introduced, and the orthogonality of the augmented eigenvectors of multi‐rigid‐flexible‐body systems is verified, which provides the readers the basic theory and techniques for solving the dynamics of linear multibody systems by using the LMSTMM. In this way, the vibration characteristics and the dynamics response of the linear multibody systems could be determined precisely, free from suffering numerical ill‐condition problems. The basic theory and the chief distinguishing features of the LMSTMM are introduced in Chapter 2. The concept of the body dynamics equations, the augmented operators, the augmented eigenvectors, and the verification of their orthogonality are provided in Chapter 3, followed by the solution of the transient dynamics response of the LMSTMM based on the mode method. The transfer matrix methods for nonlinear and multidimensional multibody systems are briefly introduced in Chapter 4.

In the first part of this book, the distinguishing features of the LMSTMM compared with traditional multibody system dynamics methods are revealed: there is no need for the global dynamics equations, the orders of the matrices involved are very low, the computational scale is rather small, the dynamics modelling is flexible, and the solution procedures are reasonably concise and suited for coding.