Reduction, Brouwer's Hamiltonian, and the critical inclination

Details Reduction, Brouwer's Hamiltonian, and the critical inclination Reduction, Brouwer's Hamiltonian, and the critical inclination

Dec 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..31..401c&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 31, Dec. 1983, p. 401-429.

Astronomy and Astrophysics

Astronomy

16

Astrodynamics, Hamiltonian Functions, Orbital Mechanics, Satellite Orbits, Angular Momentum, Celestial Mechanics, Hermitian Polynomial, Inclination, Invariance, Lagrange Multipliers

Scientific paper

The reduction process is applied twice to the Brouwer Hamiltonian of artificial satellite theory to obtain a reduced Hamiltonian MH,L on a reduced phase space PH,L which is diffeomorphic to a two-sphere. To first order in the oblateness ɛ, the reduced Hamiltonian has two nondegenerate critical points of index 2 and a nondegenerate critical circle of index 0 and the critical inclination sin2i = 4/5. To second order in ɛ, MH,L is a Morse function on PH,L with three pairs of critical points of index 0, 1, and 2, respectively.

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