Approximate integrals of motion

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.

11 pages, 11 figures, accepted for publication in Astronomy and Astrophysics

Cited by in corpus (9)

• Quasi integral of motion for axisymmetric potentials
• Spiral arm kinematics for Milky Way stellar populations
• A new dynamically self-consistent version of the Besançon Galaxy Model
• Dynamical invariants and diffusion of merger substructures in time-dependent gravitational potentials
• Integrability of motion around galactic razor-thin disks
• A simple formula for the third integral of motion of disk-crossing stars in the Galaxy
• Envelopes and vertical amplitudes of disk-crossing orbits
• Integrals of motion for non-axisymmetric potentials
• Finding stability domains and escape rates in kicked Hamiltonians