The Planar Inverse Problem of Dynamics

Chapter

Abstract

We consider the following version of the inverse problem of Dynamics: given a monoparametric family of planar curves, find the force field, conservative or not, which determines a material point to move on the curves of that family.

We present the partial differential equations which are satisfied by the potential and we clarify the role of the energy function.

Due to the nonuniqueness of the solution of the PDEs, it is natural to look for force fields in certain classes of functions (e.g., polynomial, homogeneous, or satisfying also another PDE).

In connection with the inverse problem of Dynamics, programmed motion is studied imposing the supplementary condition that the orbits lie in a preassigned region of the plane.

Applications in Celestial Mechanics, Geometrical Optics and Fluid Dynamics are given.

Keywords

Inverse problem Conservative systems Galactic potentials 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Tiberiu Popoviciu Institute of Numerical AnalysisRomanian AcademyCluj-NapocaRomania

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