Design sensitivity analysis of dynamic systems using Hamilton's law of varying action
Sensitivity vectors are computed directly from the energy equation without using the differential equations. The variations of the initial conditions have been added to the Hamilton's law through Lagrange multipliers, and the boundary conditions can be added in a similar way. The considered systems are finite degree of freedom linear systems (mass points, springs and dampers). The state variables and their variations are approximated by truncated sum of orthogonal polynomials, and in this way sparse algebraic equations were obtained. Four numerical examples are given, two with one-degree-of-freedom and two with two-degree-of-freedom systems. Results obtained by the authors' method and those calculated by Runge-Kutta integration technique show a good agreement.
scientific article; zbMATH DE number 807532