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Geometrical dynamics: A new approach to periodic orbits aroundL 4

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Abstract

Geometrical dynamics is the study of the geometry of the orbits in configuration space of a dynamical system without reference to the system's motion in time.

Generalized coordinates for the circular restricted problem of three bodies are taken as polar coordinatesr, θ centered at the triangular libration pointL 4. A time-independent nonlinear second order ordinary differential equation forr as a function of θ is derived. Approximations to periodic solutions are obtained by perturbations and Fourier series.

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Authors and Affiliations

  1. Dept. of Theoretical and Applied Mechanics, Cornell University, Ithaca, N.Y., U.S.A.

    Richard Rand (Assistant Professor) & William Podgorski (Graduate Student)

Authors
  1. Richard Rand
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  2. William Podgorski
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Rand, R., Podgorski, W. Geometrical dynamics: A new approach to periodic orbits aroundL 4 . Celestial Mechanics 6, 416–420 (1972). https://doi.org/10.1007/BF01227755

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  • DOI: https://doi.org/10.1007/BF01227755

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