Automatic Deduction Theorem of Overall Transfer Equation of Multibody System

Abstract

Transfer matrix method for multibody System (MSTMM) is a new multibody dynamics method developed in recent 20 years. It has been widely used in both science research and engineering for its special features as follows: without global dynamics equations of the system, high programming, low order of system matrix, and high computational speed. Based on MSTMM and its above features, a theorem to deduce automatically the overall transfer equations of multibody systems by handwriting or by computer is proposed in this paper. The theorem is effective for multibody systems with various topological structures, including chain systems, closed-loop systems, tree systems, general systems composed of one tree subsystem, and some closed-loop subsystems. This theorem makes it possible to program large scale software of multibody system dynamics with much higher programming, and much higher computational speed because of the above features of MSTMM. Formulations of the proposed method as well as two examples are given to verify this method.

Study On the Dynamic Modeling and the Correction Method of the Self-Propelled Artillery

“…According to the MSTMM [19], "bodies" are the units of motion, including rigid body and flexible body, "joints" are the links between bodies, including elastic joints, smooth joints, column joints, prismatic joints, fixed joints and so on. The masses of joints are considered in the contiguous bodies, so the joints are mass less, while the "bodies" and the "joints" are numbered uniformly.…”

Study on the Vibration Characteristics of a complex Multiple launch rocket system

“…According to automatic deduction theorem of overall transfer equation of multibody system [10], the overall transfer matrix of the MLRS can be deduced automatically as 5 27 23 5 27 5 26 5 27 16 5 27 13 5 27 10 5 27 7 5 27 4 5 27 1 23 23 23 16 23 13 23 10 23 7 23 4 23 1 19 16 19 1 19 13 19 1 19 10 19 1 19 7 19 1 19 4 19 1 5 28 5 25 5 28 23 5 28 5 26 5 28 16 5 28 13 5 28 10 5 28 7 5 28 4 5 28 1 12 all T C T T T T T T T T …”

“…As a brand new method for MSD gradually developed in recent 20 years, transfer matrix method for multibody system (MSTMM) [7][8][9][10] has greatly simplified the solving process of complex MSD, highly improved the computational efficiency, and provided a powerful tool for MSD study for its features as follows: without global dynamics equations of the system, high programming, low order of system matrix and high computational speed. MSTMM avoids computational ill-condition of eigenvalue problem of complex linear multiple system for its low order of system matrix.…”

“…MSTMM avoids computational ill-condition of eigenvalue problem of complex linear multiple system for its low order of system matrix. By presenting automatic deduction theorem of overall transfer equation of multibody system [10], the overall transfer equation of multibody system can be deduced automatically. MSTMM provides the theoretical basis for studying and solving the dynamics problem of complex mechanical system thus has been widely used in engineering.…”

Study on the Theory of Projectile Firing Process during Marching Fire

“…The present multibody system dynamics methods mainly include Newton-Euler vector mechanical method, Jourdam principle, Lagrange method, Gauss principle, Transfer matrix method of multibody system, and so on [15][16][17][18][19] . Taking a self-propelled artillery and tank as examples, applying the transfer matrix method for multibody system (MSTMM) and the automatic deduction theorem of overall transfer equation 20,21 , the system dynamics equations of the self-propelled artillery and tank were derived in ref. [22,23].…”