Symmetry of the first integrals in the restricted three-body problem

Details Symmetry of the first integrals in the restricted three-body problem Symmetry of the first integrals in the restricted three-body problem

Aug 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978pazh....4..326l&link_type=abstract

(Pis'ma v Astronomicheskii Zhurnal, vol. 4, July 1978, p. 326, 327.) Soviet Astronomy Letters, vol. 4, July-Aug. 1978, p. 177, 1

Astronomy and Astrophysics

Astronomy

1

Celestial Mechanics, Three Body Problem, Orbital Mechanics, Symmetry

Scientific paper

This letter demonstrates that the first integrals of the equations of motion for a zero-mass body in the restricted three-body problem in Nechvile coordinates possess certain general symmetry properties. A proof is given for the theorem that every first integral of the cited equations of motion has symmetry properties with respect to the (x, y) coordinate plane, the (x, z) coordinate plane, and the direction from which the independent variable v is measured. It is noted that the familiar Jacobi integral for the circular restricted three-body problem possesses the investigated symmetry properties and that the Hill surfaces are symmetric with respect to the (x, y) and (x, z) coordinate planes.

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