Integrals of motion for the classical two-body problem with drag
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.
second-order vector differential equation
scientific article; zbMATH DE number 3843198