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On the determination of the potential function from given orbits

L. Alboul, J. Mencía, R. Ramírez, N. Sadovskaia (2008)

Czechoslovak Mathematical Journal

The paper deals with the problem of finding the field of force that generates a given ( N - 1 )-parametric family of orbits for a mechanical system with N degrees of freedom. This problem is usually referred to as the inverse problem of dynamics. We study this problem in relation to the problems of celestial mechanics. We state and solve a generalization of the Dainelli and Joukovski problem and propose a new approach to solve the inverse Suslov’s problem. We apply the obtained results to generalize the...

On the Poincaré-Lyapunov constants and the Poincare series

Jaume Giné, Xavier Santallusia (2001)

Applicationes Mathematicae

For an arbitrary analytic system which has a linear center at the origin we compute recursively all its Poincare-Lyapunov constants in terms of the coefficients of the system, giving an answer to the classical center problem. We also compute the coefficients of the Poincare series in terms of the same coefficients. The algorithm for these computations has an easy implementation. Our method does not need the computation of any definite or indefinite integral. We apply the algorithm to some polynomial...

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