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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.

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