Design Sensitivity Analysis of Dynamic Systems

Methods for calculation of first and second design derivatives of performance measures for nonlinear dynamic systems are presented. Design sensitivity analysis formulations for dynamic systems are presented in two alternate forms; (1) equations of motion are written in terms of independent generalized coordinates and are reduced to first order form and (2) equations of motion of constrained systems are written in terms of a mixed system of second order differential and algebraic equations. Both first and second order design sensitivity analysis methods are developed, using a theoretically simple direct differentiation approach and a somewhat more subtle, but numerically efficient, adjoint variable method. Detailed derivations are presented and computational algorithms are discussed. Examples of first and second order design sensitivity analysis of mechanisms and machines are presented and analyzed.