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Mathematics Without Boundaries pp 1–29Cite as

The Planar Inverse Problem of Dynamics

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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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Authors and Affiliations

  1. Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania

    Mira-Cristiana Anisiu

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  1. Mira-Cristiana Anisiu
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Correspondence to Mira-Cristiana Anisiu .

Editor information

Editors and Affiliations

  1. Dept. Industrial & Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  2. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Anisiu, MC. (2014). The Planar Inverse Problem of Dynamics. In: Pardalos, P., Rassias, T. (eds) Mathematics Without Boundaries. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1124-0_1

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