Borisov, A.V. and García-Naranjo, L.C. and Mamaev, I.S. and Montaldi, James (2017) Reduction and relative equilibria for the 2-body problem in spaces of constant curvature. [MIMS Preprint]
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Abstract
We perform the reduction of the two-body problem in the two dimensional spaces of constant non-zero curvature and we use the reduced equations of motion to classify all relative equilibria (RE) of the problem and to study their stability. In the negative curvature case, the nonlinear stability of the stable RE is established by using the reduced Hamiltonian as a Lyapunov function. Surprisingly, in the positive curvature case this approach is not sufficient and the proof of nonlinear stability requires the calculation of Birkhoff normal forms and the application of stability methods coming from KAM theory. In both cases we summarize our results in the Energy-Momentum bifurcation diagram of the system.
Item Type: | MIMS Preprint |
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Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 70 Mechanics of particles and systems |
Depositing User: | Dr James Montaldi |
Date Deposited: | 12 Aug 2017 |
Last Modified: | 08 Nov 2017 18:18 |
URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2567 |
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- Reduction and relative equilibria for the 2-body problem in spaces of constant curvature. (deposited 12 Aug 2017) [Currently Displayed]
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