Integrals of motion for the classical two-body problem with drag
type: Item
instance of: scholarly article
title: Integrals of motion for the classical two-body problem with drag
zbMATH Open document ID: 0531.70008
DOI: 10.1016/0020-7462(83)90039-2
author: D. J. Jezewski
author: Don Mittleman
published in: International Journal of Non-Linear Mechanics
publication date: 1983-01-01T00:00:00Z
review text: The two-body problem which includes a drag acceleration is considered. \[ (1)\quad \ddot R+(\alpha \dot R/r^ 2)+(\mu R/v^ 2)=0, \] where R is a radius vector from the attracting mass to the particle, \(\alpha\) and \(\mu\) are scalar constants, \(r=| R|\). Operating directly on the second-order vector differential equation (1) that describes the motion three integrals of motion are obtained. Some other results of the authors [Celestial Mech. 28, 401-413 (1982; Zbl 0507.70004)] are used. It is also shown that when the drag coefficient \(\alpha\) approaches zero, these integrals reduce to the Keplerian energy, the vector angular momentum, and the Laplace vector.
Mathematics Subject Classification ID: 70F05
zbMATH DE Number: 3843198
zbMATH Keywords: drag acceleration
zbMATH Keywords: second-order vector differential equation
zbMATH Keywords: three integrals of motion
zbMATH Keywords: Keplerian energy
zbMATH Keywords: vector angular momentum
zbMATH Keywords: Laplace vector
MaRDI profile type: Publication
full work available at URL: 0020-7462(83)90039-2
OpenAlex ID: W2088506004
description: scientific article; zbMATH DE number 3843198