Molecular/Mechanical Dynamics Simulations With Nonholonomic Constraints

In this paper a new method of incorporating linear/nonlinear nonholonomic constraints into the mechanical/molecular dynamical systems is presented. We first introduce the mass-weighted coordinates such that acceleration and forces are scaled to have the same units, and can be operated in the same space. Then we use the projector formalism and Gauss’s principle of least constraint to derive the constraint force in the explicit form so that the equations of motion are free of Lagrange multipliers. The use of mass-weighted coordinates enable the equation of the constraint forces to be expressed in terms of first generalized inverse of constraint matrix rather than the two-time generalized inverse of matrices used in the recent works. An algorithm of numerical integration for ensuring the satisfaction of constraint equations and avoiding the numerical drift is proposed. Two simple examples, constant kinetic energy (or temperature) and time-varying prescribed kinetic energy of three-particle dynamical system effectively verify our method.