Motion near the triangular points in the elliptic restricted problem of three bodies

Details Motion near the triangular points in the elliptic restricted problem of three bodies Motion near the triangular points in the elliptic restricted problem of three bodies

Jan 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979cemec..19...31c&link_type=abstract

Celestial Mechanics, vol. 19, Jan. 1979, p. 31-41.

Physics

1

Elliptical Orbits, Equations Of Motion, Orbit Calculation, Three Body Problem, Celestial Mechanics, Hamiltonian Functions, Perturbation Theory, Variational Principles

Scientific paper

The first variational equations of motion about the triangular points in the elliptical restricted three-body problem are investigated by adopting the mean equations employed by Grebenikov (1964) as the unperturbed Hamiltonian system. The transformed Hamiltonian, including all the constant terms in eccentricity and periodic terms up to second order in the eccentricity of the primaries, is obtained. The explicit dependence of the transformed Hamiltonian on true anomaly is removed by using the perturbation theories of Hori (1966) and Deprit (1969). A general solution to the equations of motion derived from the transformed Hamiltonian is given in closed form.

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