| A molecule modelled as a collection of mass points interacting in a potential field is an important example of a Hamiltonian system. The flow of such a system possesses important geometric symplectic invariants. Symplectic discretization schemes mimic the corresponding feature of the true flow. In molecular dynamics simulations, differing timescales among the components of the potential restrict the speed of explicit symplectic integrators. This is often avoided by imposing algebraic constraints in place of the fastest components.;We generalize the techniques from constrained molecular dynamics to multi-body dynamics, producing particulation, a new formalism which offers an efficient alternative to standard approaches. Particulation algorithms are presented for discretizing continuous rigid body systems, and for modelling the interaction between bodies. Particulations are not unique, and we show that all particulations produce identical numerical dynamics. A MATLAB toolkit MBLab has been developed for the implementation of particulated multibody systems.;In this paper, commonly used symplectic discretization schemes for constrained molecular systems are discussed and the resulting nonlinear equations are shown to have a form which allows convergence results for SHAKE iteration, the traditional nonlinear solution technique from molecular dynamics. We formulate an alternative algorithm based on Successive OverRelaxation (SOR) which improves the speed of SHAKE iteration as much as twofold. Direct methods using sparse matrix techniques are proposed and shown to be superior to SHAKE and SOR for important cases. We have implemented the new techniques in the molecular dynamics package CHARMM. |
