The Projective Andoyer transformation and the connection between the 4-D isotropic oscillator and Kepler systems
Sebasti\'an Ferrer
TL;DR
This paper demonstrates a direct symplectic transformation linking the 4-D isotropic oscillator to 3-D Kepler systems, clarifying the role of the KS transformation in rectilinear solutions.
Contribution
It introduces the Projective Andoyer transformation extending attitude dynamics symplectomorphisms to connect oscillator and Kepler systems.
Findings
Established a direct symplectic link between 4-D oscillator and Kepler systems
Clarified the role of the bilinear relation in rectilinear solutions
Extended attitude dynamics transformations to higher dimensions
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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Taxonomy
TopicsStellar, planetary, and galactic studies · Astro and Planetary Science · Spacecraft Dynamics and Control