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The quasi integrals

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Abstract

The usual Von Zeipel transformations of the Hamiltonian Mechanics are presented, they lead to state functions with extremely slow variations: the ‘quasi-integrals’.

The Von Zeipel transformations are implicit: an explicit and direct construction of the quasi-integrals is also presented and the quasi-invariance property of these functions is demonstrated.

These results are applied to the problem of the motion of artificial satellites perturbed by the zonal harmonics of the Earth potential, the quasi-integral is given, it is then so constant that the problem can be considered as integrable.

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Authors and Affiliations

  1. ONERA, 92320, Châtillon, France

    C. Marchal

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  1. C. Marchal
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Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.

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Marchal, C. The quasi integrals. Celestial Mechanics 21, 183–191 (1980). https://doi.org/10.1007/BF01230896

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  • DOI: https://doi.org/10.1007/BF01230896

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