Brownian dynamics simulation of rigid bodies and segmented polymer chains. Use of Cartesian rotation vectors as the generalized coordinates describing angular orientations

The three Eulerian angles constitute the classical choice of generalized coordinates used to describe the three degrees of rotational freedom of a rigid body, but it has long been known that this choice yields singular equations of motion. The latter is also true when Eulerian angles are used in Brownian dynamics analyses of the angular orientation of single rigid bodies and segmented polymer chains. Starting from kinetic theory we here show that by instead employing the three components of Cartesian rotation vectors as the generalized coordinates describing angular orientation, no singularity appears in the configuration space diffusion equation and the associated Brownian dynamics algorithm. The suitability of Cartesian rotation vectors in Brownian dynamics simulations of segmented polymer chains with spring-like or ball-socket joints is discussed.