Towards investigation of evolution of dynamical systems with independence of time accuracy: more classes of systems

TL;DR

This paper extends a method for studying the evolution of various dynamical systems with time-independent accuracy, covering more complex systems relevant to astrophysics and cosmology.

Contribution

It develops the existing method further to include non-Hamiltonian, time-dependent, and dissipative systems, broadening its applicability.

Findings

Method now applicable to non-Hamiltonian systems

Includes systems with dissipation and time-dependent perturbations

Applicable to astrophysical and cosmological systems

Abstract

The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are much extended, now including systems that are; (1) non-Hamiltonian, conservative; (2) Hamiltonian with time-dependent perturbation; (3) non-conservative (with dissipation). These systems cover various types of N-body gravitating systems of astrophysical and cosmological interest, such as the orbital evolution of planets, minor planets, artificial satellites due to tidal, non-tidal perturbations and thermal thrust, evolving close binary stellar systems, and the dynamics of accretion disks.