Continuous transformation groups and series solution of initial value problems

This paper details an efficient method of deriving séries solutions of initial value problems traditionally encountered in non-linear mechanics. The developed technique, based on the theory of continuous transformation groups, can be used to solve autonomous as well as non-autonomous systems of ordinary differential equations. Solutions to selected problems are presented for illustration. In addition, the notion of invariants of a transformation group provides information on the nature of trajectories of an initial value problem.