Geometric Mechanics and Symmetry
Programme
Click on TITLES or scroll down to obtain lists of themes.
Click on PROGRAMME to obtain programme (when available).
Themes
Geometry and Symmetry in Continuum Mechanics
- Hamiltonian methods in fluid mechanics and elasticity theory;
the influence of symmetries.
- Multi-symplectic geometry and applications to PDEs.
- Geodesic flows on infinite dimensional Lie groups and applications.
- Integrable systems in continuum mechanics.
- Geometric integration methods for Hamiltonian continuum mechanics.
- Stability, bifurcations and dynamics of:
fluid flows, vortices, liquid crystals, elastic rods, shells,...
Back to Top
Semi-Classical and Quantum Multibody Systems
This will be a 4-5 day Spring School followed by a 4-5 day Workshop,
organized with the help of Stephen Creagh and Gregor Tanner.
- Geometry and symmetry of Hamiltonians for molecules, atoms,
nuclei ....
- Semi-classical and quantum mechanics of symmetric systems.
- Singularities: monodromy, geometric phases, ...
- Models for regular and chaotic structures in the spectra of
atoms and molecules.
Back to Top
Classical N-Body Systems and Applications
- Geometry, topology and symmetries of N-body Hamiltonians.
- The effects of symmetries on stability, bifurcations and chaotic
dynamics.
- Variational and computational methods for (relative) periodic
orbits of N-body systems.
- Geometric integrators for N-body systems.
- Applications to atoms, molecules, celestial mechanics,...
Back to Top
Astrodynamics
This will be a satellite meeting at the University of
Surrey, hosted by the
Department of Mathematics and Statistics and the
Surrey Space Centre
and organized by Tom Bridges, Phil Palmer and
Mark Roberts.
- Applications of N-body theory to satellite and space mission
trajectory design.
- Hamiltonian models for attitude and coupled
attitude-trajectory dynamics and control.
- Models of satellite formation flying.
- Computational methods: geometric integration, stable and unstable
manifolds, ...
Back to Top
Invariant and Symmetry-Preserving
Simulation Algorithms for N-Body Problems
This will be a satellite meeting hosted by the
Mathematical Modelling Centre
at the University of Leicester and organized by Ben Leimkuhler.
- Geometric (symplectic, reversible) integrators, multiple time-scale integrators
(multiple timestepping mollified methods, reversible averaging),
methods for treating close approaches in Coulombic systems,
symplectic correction methods, adaptive geometric integrators, individual timestep methods, backward error analysis of geometric integrators, and switching methods.
- Several speakers will discuss recent variational approaches, in particular as concerns their practical implementation and application.
- Connections to other related topics, such as Smoothed Particle Hydrodynamics, which often includes a gravitational component, will also be discussed.
Back to Top
Geometry of Momentum Maps and Hamiltonian Dynamics
This will be a satellite meeting hosted by the
Department of Mathematics at UMIST (Manchester) and
organized by James Montaldi.
- Topology and geometry of momentum and energy-momentum level sets.
- Bifurcations of reduced phase spaces.
- Reduction by stages.
- Applications to bifurcations and dynamics of Hamiltonian systems.
Back to Top
Geometry, Symmetry and Mechanics II
The final meeting of the Symposium and the 3rd annual meeting of the
MASIE Network.
(
GSM I was held in Lisbon: 11-17 July 2001)
- Reduction and reconstruction of symmetric Hamiltonian systems.
- Stability and bifurcations, regular and chaotic dynamics of
symmetric Hamiltonian systems.
- Applications of symplectic geometry, topology and ergodic theory
to symmetric Hamiltonian dynamics.
- Geometric control theory for symmetric Hamiltonian systems.
- Geometric numerical integration methods.
- Non-holonomic systems with symmetries.
- Applications, including N-body systems and continuum mechanics.
Back to Top