## 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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### References:

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