| EPSRC Reference: |
GR/K99893/01 |
| Title: |
RELATIVE EQUILIBRIA OF SYMMETRIC HAMILTONIAN SYSTEMS |
| Principal Investigator: |
Roberts, Professor M |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
University of Warwick |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 September 1996 |
Ends: |
31 August 2000 |
Value (£): |
98,863
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| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
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Summary on Grant Application Form |
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The principal aims of this project are to develop a bifurcation theory for relative equilibria of symmetric Hamiltonian systems and to apply it to a number of mechanical systems of physical interest including molecular models and affine rigid body molecules of atomic nuclei, elastic bodies and liquid drops. Relative equilibria of systems such as these are steady rotations during which the shape remains constant. Local bifurcation theorems, describing changes in the set of relative equilibria that occur as conserved quantities are varied, will be obtained using a combination of phase space reduction and singularity theory methods. In addition the project includes some more theoretical work on quotients of symplectic and Poisson G-manifolds that is likely to be useful in future work on the stability and nearby dynamics of relative equilibria.Apart from their intrinsic interest, these results will provide foundations for future studies of more complex dynamical behaviour in symmetric Hamiltonian systems, and for semi-classical approaches to their quantization. This would be particularly relevant to the models of molecules and atomic nuclei and it is anticipated that the results will be of interest to researchers in these areas.
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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 |
| Summary |
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| Date Materialised |
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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.warwick.ac.uk |