Approximate Conserved Quantities of Conservative Dynamical Systems in R ³

Abstract

Approximate generalized symmetries associated with the resonances of conservative dynamical systems in R ³ have been discussed. It has been shown that an approximate first integral (conserved quantities) can be found from the knowledge of two conservative approximate symmetries. Furthermore, the result has been applied to a physical system. Invariant curves have been obtained analytically and they have been compared with the numerical ones on the Poincaré surface of section. Approximate conserved quantity pinpoints the type of stability.