Approximate integrals of motion

TL;DR

This paper develops methods to find approximate integrals of motion in 2D symmetric Hamiltonian systems, enabling better modeling of regular orbits in gravitational potentials through polynomial series.

Contribution

It introduces a systematic approach to derive quasi-integrals of motion as polynomial series for specific gravitational potentials, improving orbit modeling.

Findings

Wide range of regular orbits accurately modeled

Approximate integrals as polynomial series are effective

Conditions for quasi-integrals are detailed

Abstract

We determine approximate numerical integrals of motion of 2D symmetric Hamiltonian systems. We detail for a few gravitational potentials the conditions under which quasi-integrals are obtained as polynomial series. We show that each of these potentials has a wide range of regular orbits that are accurately modelled with a unique approximate integral of motion.