The Projective Andoyer transformation and the connection between the 4-D isotropic oscillator and Kepler systems

Sebastián Ferrer

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arXiv · 1011.3000

The Projective Andoyer transformation and the connection between the 4-D isotropic oscillator and Kepler systems

Sebastián Ferrer

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Abstract

Extending to 4 degrees of freedom a symplectomorphism used in attitude dynamics it is shown in a direct way the connection between the 4-D isotropic harmonic oscillator and the 3-D Kepler systems. This approach made transparent that only when we refer to rectilinear solutions, the {\sl bilinear relation} defining the KS transformation is needed.

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Sebastián Ferrer. 2010-11-12. The Projective Andoyer transformation and the connection between the 4-D isotropic oscillator and Kepler systems. https://arxiv.org/abs/1011.3000

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