Study on automatic deduction method of overall transfer equation for branch multibody system

The transfer matrix method for multibody system is a new method developed in recent 20 years for studying multibody system dynamics. The new version of transfer matrix method for multibody system and automatic deduction theorem of system overall transfer equation have been formed in 2012. The overall transfer equation plays one of the key roles for transfer matrix method for multibody system. In order to study branch system dynamics with new version of transfer matrix method for multibody system, the automatic deduction theorem of overall transfer equation has been expanded in this article, which made it practicable to deduce automatically the overall transfer equation for branch system with new version of transfer matrix method for multibody system. The transfer equations and transfer matrices of typical elements are developed for the automatic deduction theorem of overall transfer equation. Thereby new version of transfer matrix method for multibody system owns the following features: there is no need to establish the global dynamics equation of system, by which the study on multibody system dynamics will be simplified greatly; the automatic deduction of overall transfer equation for multibody system is realized, consequently the algorithm is simple and highly programmable; moreover, the order of system matrix is always low, which result in high computational speed. The branch multibody system dynamics has been computed with the automatic deduction theorem of overall transfer equation as well as ordinary multibody system dynamics method. The computational results obtained by the two methods have good agreements, which validate the automatic deduction theorem of overall transfer equation for branch multibody system.