Non-integrability of the equation of plane oscillations of a satellite on an elliptic orbit. (Russian) Zbl 0598.70033

Burov, A. A.

Vestn. Mosk. Univ., Ser. I 1984, No. 1, 71-73 (1984).

The equation \[ (*)\quad (1+e \cos \nu){\ddot \delta}+n^ 2\sin \delta =e(4 \sin \nu +2{\dot \delta} \sin \nu),\quad n^ 2=3(A-C)/B,\quad n>0, \] models the plane oscillations of a satellite on an elliptic orbit, where e is the eccentricity, and the other parameters have known physical meaning. The author represents (*) in the form of Hamiltonian first order equations and shows that for sufficiently small \(e>0\) the Hamiltonian system does not have a real analytic first order integral.

Reviewer: G.Bojadziev

MSC:

70M20	Orbital mechanics
34C15	Nonlinear oscillations and coupled oscillators for ordinary differential equations

Keywords:

plane oscillations of a satellite; elliptic orbit; real analytic first order integral