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Reduction, Brouwer’s Hamiltonian, and the critical inclination. (English) Zbl 0559.70026

The reduction process is applied twice to the Brouwer Hamiltonian of artificial satellite theory to obtain a reduced Hamiltonian \(M_{H,L}\) on a reduced phase space \(P_{H,L}\) which is diffeomorphic to a two- sphere. To first order in the oblateness \(\epsilon\), the reduced Hamiltonian has two nondegenerate critical points of index 2 and a nondegenerate critical circle \({\mathcal C}\) of index 0 at the critical inclination \(s^ 2=4/5\). To second order in \(\epsilon\), \(M_{H,L}\) is a Morse function on \(P_{H,L}\) with three pairs of critical points of index 0,1, and 2, respectively.

MSC:

70M20 Orbital mechanics
70H05 Hamilton’s equations
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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