The discrete time transfer matrix method for multibody systems (MSDTTMM) is introduced in this part (Chapters 7 to 11). This method is used to solve multi‐rigid‐body system dynamics, multi‐rigid‐flexible‐body system dynamics and controlled multibody system dynamics. In Chapter 7, the discrete time transfer matrix method for multi‐rigid‐body systems is introduced. The discrete time transfer matrix method for multi‐rigid‐flexible‐body systems is given in Chapter 8. The transfer matrix method for controlled multibody systems and the mixed transfer matrix method as well as other methods are presented in Chapter 9. The derivation and computation method for transfer matrices is introduced in Chapter 10. The theorem to deduce the overall transfer equation automatically is introduced in Chapter 11.

The MSDTTMM can be used to compute the dynamics of general multibody systems that are time‐variant and nonlinear, and have large motion and control. This method has the following features: no global dynamic equation of the system, low order of matrix, small computational scale, modeling flexibility and high programmability. It can be used with any mechanical method, including all kinds of multibody system dynamics. The basic theory and characteristics of the MSDTTMM are introduced in this part. The efficiency and feasibility of the proposed method are validated by some numerical examples compared with other dynamic methods. In the MSDTTMM, the dynamic equations of elements are linearized and discretized in the time domain. The defined state vector is different from the transfer matrix method for linear multibody systems, and even the elements of state vectors at the two ends of a joint are different in some cases. This is because the state vector of linear multibody systems is denoted by modal coordinate parameters, but in the MSDTTMM only the state vectors of flexible bodies and joints connecting flexible bodies contain generalized coordinates corresponding to modal coordinates. For instance, the definition of the state vectors of the input and output ends of a joint connecting a rigid body and a flexible body are different in the MSDTTMM, but in the transfer matrix method for linear multibody systems they are the same.

The essential difference between the MSDTTMM and the transfer matrix method for linear multibody systems is that the transfer matrix for the latter is a constant matrix, while the transfer matrix in the MSDTTMM is time variant. The state variables of state vectors in the MSDTTMM are physical coordinate parameters (system motion) corresponding to the positions of the connection points, while for the latter they are physical coordinate parameters (steady‐state response) or modal coordinate parameters (eigenvalue problem) with respect to displacement.