Symplectic reduction and topology for applications in classical molecular dynamics

Symplectic reduction and topology for applications in classical molecular dynamics

This paper aims to introduce readers with backgrounds in classical molecular dynamics to some ideas in geometric mechanics that may be useful. This is done through some simple but specific examples: (i) the separation of the rotational and internal energies in an arbitrarily floppy N-body system and (ii) the reduction of the phase space accompanying the change from the laboratory coordinate sys...

Model reduction in classical molecular dynamics

On Symplectic Reduction in Classical Mechanics

This Chapter expounds the modern theory of symplectic reduction in finitedimensional Hamiltonian mechanics. This theory generalizes the well-known connection between continuous symmetries and conserved quantities, i.e. Noether’s theorem. It also illustrates one of mechanics’ grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. The exposition emp...

Symplectic reduction , geometric phase , and internal dynamics in three - body molecular dynamics

Symplectic reduction of the planar dynamics of a non-collinear triatomic molecule leads eventually to an internal phase space with symplectic dynamics in the bond lengths and bond angle. For the overall and internal angular velocities, the dynamic and geometric phases describe conditions for the separation of energies and separation of dynamics. @ 1997 Published by Elsevier Science B.V.

Symplectic quaternion scheme for biophysical molecular dynamics

Massively parallel biophysical molecular dynamics simulations, coupled with efficient methods, promise to open biologically significant time scales for study. In order to promote efficient fine-grained parallel algorithms with low communication overhead, the fast degrees of freedom in these complex systems can be divided into sets of rigid bodies. Here, a novel Hamiltonian form of a minimal, no...