Abstract
We describe the Hamiltonian reduction of a time-dependent real-symmetric N×N matrix system to free vector dynamics, and also provide a geodesic interpretation of Ruijsenaars–Schneider systems. The simplest of the latter, the goldfish equation, is found to represent a flat-space geodesic in curvilinear coordinates.
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Arnlind, J., Bordemann, M., Hoppe, J. et al. Goldfish Geodesics and Hamiltonian Reduction of Matrix Dynamics. Lett Math Phys 84, 89–98 (2008). https://doi.org/10.1007/s11005-008-0232-0
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DOI: https://doi.org/10.1007/s11005-008-0232-0