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On the averaging principle for one-frequency systems. An application to satellite motions

Carlo Morosi·Livio Pizzocchero
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Abstract

This paper is related to our previous works [1][2] on the error estimate of the averaging technique, for systems with one fast angular variable. In the cited references, a general method (of mixed analytical and numerical type) has been introduced to obtain precise, fully quantitative estimates on the averaging error. Here, this procedure is applied to the motion of a satellite in a polar orbit around an oblate planet, retaining only the J_2 term in the multipole expansion of the gravitational potential. To exemplify the method, the averaging errors are estimated for the data corresponding to two Earth satellites; for a very large number of orbits, computation of our estimators is much less expensive than the direct numerical solution of the equations of motion.

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Carlo Morosi, Livio Pizzocchero. 2009-02-26. On the averaging principle for one-frequency systems. An application to satellite motions. https://doi.org/10.1007/s11071-009-9477-0

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