VARIATIONAL CALCULUS AND APPROXIMATE SOLUTIONS OF DIFFERENTIAL EQUATIONS

摘要

Variational calculus is a differential process whereby Taylor series expansions can be developed on a term by term basis. Therefore, it can be used to obtain the equations which must be solved for the various-order terms arising from the application of regular perturbation theory to problems involving a small parameter. Variational calculus is developed for ordinary differential equations and applied to the approximate analytical solution of the regular perturbation problem. Its use for deriving the equations for the various-order solutions is demonstrated for the initial value problem with fixed final time and the initial value problem with free but constrained final time. As an example, the problem of satellite motion in the equatorial plane of an oblate spheroid earth with small eccentricity is discussed.