Quadratic Hamilton-Poisson Systems on $\mathfrak{so}^*_{-}(3)$: Classification and Integration

Adams, Ross M.; Biggs, Rory; Remsing, Claudiu C.

doi:10.7546/giq-15-2014-55-66

VOL. 15 | 2014 Quadratic Hamilton-Poisson Systems on $\mathfrak{so}^*_{-}(3)$: Classification and Integration

Chapter Author(s) Ross M. Adams, Rory Biggs, Claudiu C. Remsing

Editor(s) Ivaïlo M. Mladenov, Andrei Ludu, Akira Yoshioka

Geom. Integrability & Quantization, 2014: 55-66 (2014) DOI: 10.7546/giq-15-2014-55-66

Abstract

We classify, under affine equivalence, the quadratic Hamilton-Poisson systems on the Lie-Poisson space $\mathfrak{so}^*_{-}(3)$. For the simplest strictly inhomogeneous quadratic system, we find explicit expressions for the integral curves in terms of Jacobi elliptic functions.