On evolutionary motions of a particle in a gravitational field
type: Item
instance of: scholarly article
title: On evolutionary motions of a particle in a gravitational field
zbMATH Open document ID: 0628.70005
DOI: 10.1016/0021-8928(86)90120-6
published in: Journal of Applied Mathematics and Mechanics
publication date: 1986-01-01T00:00:00Z
review text: Non-conservative, time-periodic perturbations of the Kepler problem are studied. A phase-averaged system is given, which determines the evolution in the system when there are no resonance modes. The qualitative behaviour of the solutions in the resonance zones is studied. Depending on the structure of the behaviour of the solutions, the resonances are divided into traversable, partially traversable and non-traversable. The boundedness of the set of partially traversable resonances is established, and this, in many cases, makes it possible to determine evolution in a system with resonance modes. An example is used to illustrate the method. It is shown that a constant component in the periodic function of the perturbation causes the evolutionary process to become non-unidirectional.
Mathematics Subject Classification ID: 70F05
Mathematics Subject Classification ID: 70K20
Mathematics Subject Classification ID: 70C20
zbMATH DE Number: 4022681
zbMATH Keywords: Non-conservative, time-periodic perturbations
zbMATH Keywords: Kepler problem
zbMATH Keywords: phase- averaged system
zbMATH Keywords: resonance modes
author: Albert D. Morozov
MaRDI profile type: Publication
full work available at URL: 0021-8928(86)90120-6
OpenAlex ID: W2088036252
cites work: Q5338214
cites work: Q5548232
cites work: Q3925907
cites work: On nonconservative periodic systems close to two-dimensional Hamiltonian
cites work: Q5640781
cites work: A General Theory of Resonance Between Weakly Coupled Oscillatory Systems
cites work: On resonances in systems of two weakly coupled oscillators
description: scientific article; zbMATH DE number 4022681