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On the construction of dynamic systems from given integrals

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Abstract

In this communication we propose a new approach for studying a particular type of inverse problems in mechanics related to the construction of a force field from given integrals.

An extension of the Danielli problem is obtained. The given results are applied to the Suslov problem, and illustrated in specific examples.

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References

  1. Bertrand, M. J.: Sur la possibilité de deduire d'une seule des lois de Kepler le principe de l'attraction,C.R. Acad. Sci. Paris 9 (1877).

  2. Danielli, V.:Giornale di Mat.,18 (1880), 271.

    Google Scholar 

  3. Darboux, M. G.: Recherche de la loi que doit suivre une force centrale pour que la trajectorie quelle détermine soit toujours une conique,C.R. Acad. Sci. Paris 16 (1877).

  4. Galiullin, A. S.:Inverse Problems in Dynamics, Nauka, Moscow, 1981 (in Russian).

    Google Scholar 

  5. Joukovski, N. E.: The determination of the potential function by given trajectories, Sobranie Sochinieni, Vol. 1, M.-L., Gostexizdat, (1948), pp. 227–242 [in Russian].

  6. Ramirez, Rafael and Sadovskaia, Natalia: Construction of vector fields by given first integrals,Collectanea Mathematica 40(3) (1989) [in Spanish].

  7. Suslov, G. K.: The potential function with given partial integrals, Kiev (1890) [in Russian].

  8. Szebely, V.: On the determination of the potential,E. Proverbio, Proc. Int. Mtg. Rotation of the Earth, Bologna (1974).

  9. Whittaker, E. T.:Analytical Dynamics of Particles and Rigid Bodies, Cambridge University, Cambridge, MA (1959).

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Ramirez, R., Sadovskaia, N. On the construction of dynamic systems from given integrals. Celestial Mech Dyn Astr 63, 149–170 (1995). https://doi.org/10.1007/BF00693411

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  • DOI: https://doi.org/10.1007/BF00693411

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