Celestial Mechanics and Dynamical Astronomy

, Volume 60, Issue 1, pp 161–172 | Cite as

Family boundary curves for autonomous dynamical systems

  • George Bozis


The notion of the family boundary curves (FBC), introduced recently for two-dimensional conservative systems, is extended to account for, generally, nonconservative autonomous systems of two degrees of freedom. Formulae are found for the force componentsX (x, y),Y (x, y) which produce a preassigned family of orbitsf(x, y)=c lying inside a preassigned, open or closed, regionB(x, y)≥0 of the xy plane.

Key words

inverse problem family boundary curves 


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  1. Bozis, G.: 1983,Inverse Problem with Two-Parametric Families of Planar Orbits, Celest. Mech.31, 129Google Scholar
  2. Bozis, G. and Ichtiaroglou, S.: 1994,Boundary curves for families of planar orbits, Celest. Mech.58, 371Google Scholar
  3. Kasner: Differential Geometric Aspects of Dynamics, Princeton Colloquium 1909, New York, AMS 1913 (Reprinted 1933)Google Scholar
  4. Puel, F.: 1988,Three Dimensional Equations of Szebehely of the Inverse Problem and Frenet Reference Frame, in “Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems” (ed. by A.E. Roy), p.471Google Scholar
  5. Puel, F., 1992,Explicit Solution of the Three Dimensional Inverse Problem of Dynamics using the Frenet Reference Frame, Celest. Mech.53, 207Google Scholar
  6. Szebehely, V.: 1974,On the Determination of the Potential by Satellite Observation, Rend. Sem. Fac. Sc. Univ. Cagliari, XLIV, Suppl. 31–35Google Scholar
  7. Whittaker, E.T.: A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge Univ. Press. 4th Edition, 1944, p.21 (Reprint)Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • George Bozis
    • 1
  1. 1.Department of Theoretical MechanicsUniversity of ThessalonikiThessalonikiGreece

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