Computer Algebraic Manipulation for the Calculus of Variations, The Maximum Principle, and Automatic Control

摘要

This report describes how to use a computer algebra system such as MACSYMA to solve variational optimization problems analytically. For a calculus of variations problem, the user merely provides expressions for the integrand of the functional and any constraints. From these expressions, a program derives the specific Euler-Lagrange equations together with first integrals when the augmented functional is free of the independent and/or any dependent variables. Other programs may then be used to construct families of analytical solutions to these differential equations and to obtain the particular solutions that satisfy given boundary conditions.