1 Radu Serban and Edward J. Haug Department of Mechanical Engineering The University of Iowa Iowa City, Iowa 52242–1000, USA ANALYTICAL DERIVATIVES FOR MULTIBODY SYSTEM ANALYSES ABSTRACT Analytical formulas for kinematic and kinetic derivatives needed in multibody system analyses are derived. A broad spectrum of problems, including implicit numerical integration, dynamic sensitivity analysis, and kinematic workspace analysis, require evaluation of first derivatives of generalized inertia and force expressions and at least three derivatives of algebraic constraint functions. In the setting of a formulation based on Cartesian generalized coordinates with Euler parameters for orientation, basic identities are developed that enable practical and efficient computation of all derivatives required for a large number of multibody mechanical system analyses. The formulation is verified through application to to a spatial slider crank mechanism and a 14 body vehicle model. Efficiency of computation using the expressions derived is compared with results obtained employing finite differences, showing significant computational advantage using the analytically derived expressions. 1 INTRODUCTION Three different areas of multibody system analysis are considered. The common requirement for numerical methods used in these types of analysis is the availability of higher order derivatives of both the differential equations of motion and of the algebraic constraint equations. The three types of analysis under consideration are as follows: (1) numerical implicit integration of the differential–algebraic equations (DAE) of motion for simulation of stiff mechanical systems; (2) dynamic sensitivity analysis for design optimization, parameter estimation, and model correlation; (3) kinematic workspace analysis of mechanisms. Next, each of these problems is shortly described and required derivatives for numerical solution are identified.