The Hill determinant of a periodic orbit

Details The Hill determinant of a periodic orbit The Hill determinant of a periodic orbit

Jun 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988mvsmm.......30b&link_type=abstract

Moskovskii Universitet, Vestnik, Seriia 1 - Matematika, Mekhanika (ISSN 0579-9368), May-June 1988, p. 30-34. In Russian.

Physics

Celestial Mechanics, Hill Lunar Theory, Trajectory Analysis, Functionals, Hermitian Polynomial, Hill Determinant

Scientific paper

Hill reduced the determination of the characteristic indices of the Hill equation in lunar theory to the calculation of an infinite determinant. In the present paper, this result is extended to the multidimensional case. It is shown that the characteristic polynomial of the periodic orbit of a Lagrangian mechanical system can be expressed through the generalized hessian of the Hamiltonian action functional at the appropriate critical point.

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