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Orbital stability of stationary satellites. (Spanish. English summary) Zbl 0900.70376

Summary: For a satellite around an oblate planet in rotation around its axis of greatest inertia, conditions are given under which there may appear, in a frame fixed in the planet, two positions of equilibrium with characteristic exponents that are purely imaginary. For this case, after appropriate normalization by Lie transformation mechanically through a symbolic algebraic processor, the Arnold theorem about non-definite quadratic forms is applied. lt is concluded that the equilibria are stable in the sense of Lyapunov. The conditions for stability are verified in the case of the Earth.

MSC:

70M20 Orbital mechanics
70K20 Stability for nonlinear problems in mechanics
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