Coefficients of an Averaged Equation of Satellite Oscillations.
Abstract:
We consider an averaged equation of oscillations of an almost symmetric satellite in a plane of its elliptic orbit with the eccentricity e close to 1. The right-hand side of the equation is a series in powers of a small parameter μ. We study analytically the behaviour of its coefficients at powers of μ up to the third one as e → 1. A regular for e ≈ 1 method of computing the coefficients is offered. Obtained results are applied for finding the bifurcation line (i.e. the boundary of the of stability region of odd periodic solutions), which enters the point μ = 0, e = 1.
