Unifying the Hyperbolic and Spherical -Body Problem with Biquaternions.

Autor: Arathoon, Philip
Zdroj: Regular & Chaotic Dynamics; Nov2023, Vol. 28 Issue 6, p822-834, 13p
Abstrakt: The -body problem on the sphere and hyperbolic space are both real forms of holomorphic Hamiltonian systems defined on the complex sphere. This admits a natural description in terms of biquaternions and allows us to address questions concerning the hyperbolic system by complexifying it and treating it as the complexification of a spherical system. In this way, results for the -body problem on the sphere are readily translated to the hyperbolic case. For instance, we implement this idea to completely classify the relative equilibria for the -body problem on hyperbolic 3-space and discuss their stability for a strictly attractive potential. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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