Design sensitivity analysis of dynamic systems using Hamilton's law of varying action

Abstract

Hamilton's law of varying action (HLVA) is used to compute design sensitivity of dynamic systems. The state variables and their variations are approximated using truncated linear sums of orthogonal polynomials and the integral equations are converted to algebraic equations. The orthogonal properties of these polynomials are utilized to make these algebraic equations sparse and thus computationally efficient. This formulation leads to a reduction on the continuity requirement on the states. Four examples are solved to demonstrate the efficacy of this method. Methods to include the state sensitivity to static initial conditions are presented. For comparison, the problems are also solved using the Runge-Kutta integration scheme. Good agreement is found between the two techniques.