Abstract
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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References
Goudas, G., Nature, 218, 726 (1968).
Contopoulos, G., Astron. J., 72, 669 (1967).
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CONTOPOULOS, G. New Integrals of Motion and the Orbital History of the Moon. Nature 220, 1018 (1968). https://doi.org/10.1038/2201018a0
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DOI: https://doi.org/10.1038/2201018a0
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