Second-order sensitivity analysis of multibody systems described by differentialz/algebraic equations: Adjoint variable approach

A second-order sensitivity analysis has higher accuracy and can improve convergence of optimization design, but its computation is complex. This paper studies the adjoint variable method of second sensitivity analysis for multibody system dynamics described by second-order differential/algebraic equations. Based on general objective function, constraint conditions, initial and end conditions, the adjoint variable equations for first-order sensitivity analysis and design sensitivity formulations are derived first, then second-order sensitivity analysis formulations are set up based on the previous results. For simplification, the second derivative of the objective function is transformed to an initial value problem of an ordinary differential equation with one variable. Finally, the comparison between the results of direct computation, first-order sensitivity and second-order sensitivity validate the method presented in this paper.