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

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
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