Rotational Motion

Abstract

An asymmetric top under the influence of time dependent external forces is a rather complicated subject in mechanics. Efficient methods to describe the rotational motion are important as well in astrophysics as in molecular physics. The orientation of a rigid body relative to the laboratory system can be described by a 3×3 matrix. Instead of solving nine equations for all its components, the rotation matrix can be parametrized by the four real components of a quaternion. Euler angles use the minimum necessary number of three parameters but have numerical disadvantages. Care has to be taken to conserve the orthogonality of the rotation matrix. Omelyan’s implicit quaternion method is very efficient and conserves orthogonality exactly. In computer experiments we compare different explicit and implicit methods for a free rotor, we simulate a rotor in an external field and the collision of two rotating molecules.