Equivalence of Two Order (N) Rate Solutions for Multibody Systems with Hamilton's Equations Based Eom

Martin Tong

《Proceedings of the 14th IFToMM World Congress》 14th-3 (2015/10) Pp. 28-35

https://doi.org/10.6567/IFToMM.14TH.WC.OS11.004

並列摘要

Order (N) rate solution for rigid multibody systems whose equations of motion (eom) are derived from Hamilton's equations has been presented in the recent past. Order (N) means that the computational effort of that solution is proportional to N, number of bodies in the system. The method of this solution is a recursive algorithm similar to that by Brandl (1988) in solving accelerations from the Newton-Euler equations based eom. An alternate closed form order(N) rate solution for the same problem has also been published, where the derivation method is similar to that of Rodriguez et.al (1992) in using their the Spatial Operator Algebra (SOA) for the same problem Brandl addressed. While the two rate solutions are equivalent intuitively, the proof of that equivalence has not been demonstrated. This paper has that proof in mind. In particular, it will show the derivation of the closed form order (N) rate solution from implicit rate equations of the recursive algorithm.

並列關鍵字

closed form ； recursive ； order(N) ； rate solution ； multibody