Astronomy and Astrophysics – Astronomy
Scientific paper
Feb 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977sval....3...23r&link_type=abstract
(Pis'ma v Astronomicheskii Zhurnal, vol. 3, Jan. 1977, p. 43-46.) Soviet Astronomy Letters, vol. 3, Jan.-Feb. 1977, p. 23, 24. T
Astronomy and Astrophysics
Astronomy
Equations Of Motion, Inequalities, Jacobi Integral, Three Body Problem, Boundary Value Problems, Differential Equations
Scientific paper
The plane version of the general three-body problem in Jacobi coordinates is examined. It is shown that the Sundman inequality is a consequence of the integrals of motion in the general problem and that this inequality is transformed into an equality during all Lagrangian motions of a three-body system. The Jacobi integral of the circular restricted three-body problem is derived from the integrals of motion in the general problem as the passage to the limit where the mass of one body tends to zero while the motion of the other two bodies approaches circular motion.
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