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Solution of an inverse problem of the dynamics of a particle

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Abstract

The three-dimensional inverse problem of particle dynamics is studied here. The potentialU and the corresponding energyh are determined by the given family of possible trajectories. The classification of the solutions due to the geometry of the given family is obtained.

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References

  • Bertrand, J.: 1877, ‘Sur la possibilité de déduire d'une seule des lois de Kepler le principe de l'attraction’,Compt. Rend.,84 671.

    Google Scholar 

  • Bozis, G.: 1983, ‘Generalization of Szebehely's Equations’,Celest. Mech.,29, 329.

    Google Scholar 

  • Bozis, G.: 1984, ‘Szebehely's Inverse Problem for Finite Symmetrical Material Concentrations’,Astron. Astrophys.,134, 360.

    Google Scholar 

  • Bozis, G. and Nakhla, A.: 1986, ‘Solution of the Three-Dimensional Inverse Problem’,Celest. Mech.,38, 357.

    Google Scholar 

  • Bulatskaya, T. F.: 1977, ‘Determination of Force Functions from Given Properties of Motion’,Diff. Equat.,13, 1222.

    Google Scholar 

  • Dainelli, U.: 1880, ‘Sul movimento per una, linea qualunque’,Giorn. Mat.,18, 271.

    Google Scholar 

  • Ermakov, V. P.: 1891, ‘Bestimmung der Kräftefunction bei gegebenen Integralen’,Recueil Math.,15, 611.

    Google Scholar 

  • Erugin, N. P.: 1952, ‘Construction of the Totality of Systems of Differential Equations, Possessing Given Integral Curve’,PMM,16, 659 (in Russian).

    Google Scholar 

  • Galiullin, A. S.: 1981, ‘Construction of a Field of Forces by a Given Family of Trajectories’,Diff. Equat.,17, No. 8

    Google Scholar 

  • Galiullin, A. S.: 1984,Inverse Problems of Dynamics, Mir Publishers, Moscow, Ch. 1, p. 16.

    Google Scholar 

  • Galiullin, A. S.: 1986,Methods of Solution of Inverse Problem of Dynamics, Nauka, Moscow, Ch. 4, p. 122 (in Russian).

    Google Scholar 

  • Hearn, A. C.: 1983,REDUCE User's Manual: Version 3.0, Santa Monica, Rand Publication CP78(4/83), p. 1–1.

  • Ichtiaroglou, S. and Bozis, G.: 1985, ‘Stability of Circular Orbits in Non-Central Newtonian Fields’,Astron. Astrophys.,151, 64.

    Google Scholar 

  • Imshenetsky, V. G.: 1882, ‘Détermination en fonction des coordonnées de la force qui fait mouvoir un point matériel sur une section conique’,Mém. Soc. Sci. Bordeaux,4, 31.

    Google Scholar 

  • Joukovsky, N. E.: 1890, ‘Determination of Force Function by Given Family of Trajectories’,Izv. Imper. Obsch. Lubit. Estestv.,65, No. 2, 43 (in Russian).

    Google Scholar 

  • Melis, A. and Borghero, F.: 1986, ‘On Szebehely's Problem Extended to Holonomic Systems with a Given Integral of Motion’,Meccanica,21, 71.

    Google Scholar 

  • Melis, A. and Piras, B.: 1982, ‘On a Generalization of Szebehely's Problem’,Rend. Sem. Fac. Sci. Univ. Cagliari,52, 73.

    Google Scholar 

  • Newton, I.: 1687,Philosophiae Naturalis Principia Mathematica, London.

  • Orlov, A. I.: 1983, ‘Construction of a Force Function with Respect to a Given Family of Trajectories’,Diff. Equat.,19, No. 10.

    Google Scholar 

  • Orlov, A. and Ramirez, R.: 1983, ‘On the Construction of the Potential Function from a Preassigned Family of Particular Integrals’,Hadronic Journal,6, 1705.

    Google Scholar 

  • Ramirez, R.: 1983, ‘On the Construction of a Force Function with Respect to Given Particular Integrals’,Diff. Equation.,19, No. 6.

    Google Scholar 

  • Singatullin, R. S.: 1983, ‘Reconstruction of the Gravitational Field Determined by the Direction Field in a Three-Dimensional Fok's Space from Some Trajectories’,IVUZ FIZ,26, No. 4, 37.

    Google Scholar 

  • Suslov, G. K.: 1890, ‘On the Force Function, Admitting Given Particular Integrals' (Doctor Thesis), Univ. Izv. (Kiev), 30, No. 8, 1–114 (in Russian).

    Google Scholar 

  • Szebehely, V.: 1961, ‘The Generalized Inverse Problem of Orbit Computation’, inProc. 2nd Intern. Space Sci. Symp., North-Holland Publ., Amsterdam, v. 3, 318.

    Google Scholar 

  • Szebehely, V.: 1974, ‘On the Determination of the Potential by Satellite Observations’,Rend. Fac. Sci. Univ. Cagliari,44, suppl., 31.

    Google Scholar 

  • Szebehely, V. and Broucke, R.: 1981, ‘Determination of the Potential in a Synodic System’,Celest. Mech.,24, 23.

    Google Scholar 

  • Váradi, F. and Érdi, B.: 1983, ‘Existence of the Solution of Szebehely's Equation in Three Dimensions Using a Two-Parametric Family of Orbits’,Celest. Mech.,30, 395.

    Google Scholar 

  • Whittaker, E. T.: 1944A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Dover Publ., New York, Ch. IV, p. 96.

    Google Scholar 

  • Shorokhov, S. G.: 1987, ‘On the Motion of Mechanical System in Potential Force Fields’,Trudy VZIIT, No. 134, 167 (in Russian).

    Google Scholar 

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Authors and Affiliations

  1. Department of Theoretical Mechanics, Moscow Friendship University, USSR

    S. G. Shorokhov

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  1. S. G. Shorokhov
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Shorokhov, S.G. Solution of an inverse problem of the dynamics of a particle. Celestial Mechanics 44, 193–206 (1988). https://doi.org/10.1007/BF01230715

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  • DOI: https://doi.org/10.1007/BF01230715

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