Rigid Body Molecular Dynamics Algorithm

To develop an integrator for the complete system (including external forces), we invoke the splitting technique, solving successively for the translational motion from the center of mass equations, integrating the torques due to the rotational interactions, then solving the Euler equations, and recovering the rotation matrix from the linear system 

This is the approach described in [112] and is implemented in several software 

The reliability of these methods is supported by the fact that the combined scheme is a symplectic method in the generalized sense of constrained dynamics. 

The specific steps of the algorithm proposed in [112] are given here. In what follows, we denote the variables associated to the Mi rigid body by (position of center of mass), 0 (3 x 3 rotation matrix), / (linear momentum vector), and jr (angular momentum vector). Individual components are defined by double subscripts the 2nd component of jt is jt. Procedures given below for rigid body k are meant to be performed for all rigid bodies in the system. 

The algorithm is initialized by computing the forces F and torques t acting on the Ml rigid body, evaluated at the initial point. The relevant expressions are  

---