| EPSRC Reference: |
GR/R70736/01 |
| Title: |
Stability of Hamiltonian Relative Equilibria |
| Principal Investigator: |
Roberts, Professor M |
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| Department: |
Sch of Electronics & Physical Sciences |
| Organisation: |
University of Surrey |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
24 January 2002 |
Ends: |
23 September 2002 |
Value (£): |
4,424
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Mathematical Analysis |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Relative equilibria are trajectories which reduce to equilibria in appropriate rotating or translating frames. They provide important organising centres for more complex dynamics in systems such as molecules, gravitational N-body problems, space and underwater vehicles, and fluids. The nonlinear stability of a Hamiltonian relative equilibrium is typically determined using energy-momentum methods. These are well developed for compact symmetr groups, but are only currently being extended to non-compact groups, such as Eudidean groups. The first aim of this project is to extend results of Patrick, Roberts and Wulff on the energy-momentum method for free actions of non-compact groups to general proper actions, and in particular to investigate how isotropy facilitates the application of these methods. The second aim is to develop alternatives to the energy-momentum method for when these fail, either because a definiteness criterion is not satisfied or, more fundamentally, because the relative equilibrium is not the critical point o any conserved function on the subset of phase space in which the dynamics has to be controlled. The main aim here will be to obtain Nekhoroshev stability estimates.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.surrey.ac.uk |