New Integrals of Motion and the Orbital History of the Moon

Details New Integrals of Motion and the Orbital History of the Moon New Integrals of Motion and the Orbital History of the Moon

Dec 1968

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1968natur.220.1018c&link_type=abstract

Nature, Volume 220, Issue 5171, pp. 1018 (1968).

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GOUDAS1 has criticized the integrals of motion that I have given2 for the elliptic restricted three body problem. He states: ``Contopoulos has given an integral equivalent to the Jacobi integral for the elliptic restricted problem as well as one additional time-independent integral for the same equations of motion. It seems, however, that the work of Contopoulos is not in harmony with a famous theorem by Poincaré'' because ``if two integrals, time-independent and independent of one another, exist, then there should be two zero characteristic exponents associated with each periodic solution'', which is not the case.

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