Concerning Integrals of the Motion for the Restricted Three Body Problem Linearized about L4 and L5

Details Concerning Integrals of the Motion for the Restricted Three Body Problem Linearized about L4 and L5 Concerning Integrals of the Motion for the Restricted Three Body Problem Linearized about L4 and L5

Sep 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998dda....30.0602c&link_type=abstract

American Astronomical Society, DDA meeting #30, #06.02; Bulletin of the American Astronomical Society, Vol. 30, p.1142

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Isolating integrals of the equations of motion for the restricted three body problem are studied when the equations are linearized about L4 and L5. There is a complete set of 3 isolating integrals for the motion in the orbit plane of the large bodies ( the 2 body plane ). There are 2 independent quadratics in the kinematic variables which are integrals of Jacoby and Khorseva specialized to this situation. It is shown that there are 2 independent linear combinations of these quadratic integrals which are positive definite. A 3rd integral is found which is not quadratic but which can be expressed in terms of elementary functions of the kinematic variables. When 3 dimensional motion is considered in the above linearized context, there is another known isolating integral which expresses conservation of energy for motion perpendicular to the 2 body plane. A general statistical treatment of the linearized motion near L4 and L5 in the restricted three body problem is possible since stellar dynamics guarantees that for a motion with 6 degrees of freedom a general distribution function need only involve 4 independent isolating integrals.

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