Analytical fully-recursive sensitivity analysis for multibody dynamic chain systems (Q1610824)

A fully recursive sensitivity analysis method is presented to provide the first-order sensitivity information in optimal design of multibody chain systems. The algorithm is based on a velocity space projection method, promoted by \textit{T. R. Kane} and \textit{D. A. Levinson} [Dynamics, theory and applications, McGraw-Hill, New York (1985)]. The use of recursive algorithm can reduce the massive number of computational operations exhibited in traditional direct differentiation approaches. The comparison of CPU times for fully recursive method and for the direct approach or finite difference approach is given, and the simulation of sensitivity time history of a double pendulum is demonstrated as numerical example.