Eur. Phys. J. C (2015) 75: 332
https://doi.org/10.1140/epjc/s10052-015-3560-0

Regular Article - Theoretical Physics

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

¹ SIA, Sapienza University of Rome, Rome, Italy
² Center for Cosmology and Astrophysics, Alikhanian National Laboratory and Yerevan State University, Yerevan, Armenia
³ School of Mathematical Sciences, Monash University, Clayton, Australia

^* e-mail: gurzadyan@yerphi.am

Received: 17 May 2015
Accepted: 6 July 2015
Published online: 17 July 2015

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.