Nonlinear stability of the triangular libration points for the photogravitational elliptic restricted problem of three bodies

Details Nonlinear stability of the triangular libration points for the photogravitational elliptic restricted problem of three bodies Nonlinear stability of the triangular libration points for the photogravitational elliptic restricted problem of three bodies

Dec 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990cemda..48..299k&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 48, no. 4, 1990, p. 299-317.

Statistics

Computation

2

Hamiltonian Functions, Libration, Orbital Resonances (Celestial Mechanics), Three Body Problem, Computational Astrophysics, Gravitational Effects

Scientific paper

Kumar and Choudhry (1988) demonstrated the existence of third- and fourth-order resonances within the linear stability range in the context of the photogravitational elliptical restricted three-body problem. Here, the stability of the libration points in these resonances is investigated analytically, assuming that the second-order terms in the Hamiltonian have already been normalized by the method of Birkhoff. The derivation is given in detail, and it is concluded that, for small values of the parameter e, the character of the motion will continue to be the same as for the circular case. The stability for cases where the resonances are not present is also briefly discussed.

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