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Singularities of oscillations of a satellite on highly eccentric elliptic orbits. (English) Zbl 0898.34034
Singularities of an equation describing oscillations of a satellite with respect to its mass center are considered \[ (1+e\cos V) \;{{d^2\delta}\over{dV^2}}-2e\sin V\;{{d\delta}\over{dV}}+\mu \sin\delta =4e\sin V . \] Here \(\delta \) is the doubled angle between the radius vector of the mass center of the satellite and one of its axis of inertia; \(\mu \) is the inertial parameter of the satellite; \(e\) is the eccentricity of the orbit; \(V\) is the true anomaly of the position of the satellite on the orbit; \(e\leq 1\), \(| \mu | \leq 3\). It is regular if \(e<1\). For \(e=1\) and \(V=\pi \), it is singular since the coefficient of the higher derivative vanishes. In this case the study of the motion as function of \(\mu \) is reduced to a study of three limit equations, named basic, first and second. The dynamics of the system is completely studied.

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