ABSTRACT
For a non-magnetic spherical particle system, for symmetry reasons, it is not necessary to specify the orientational situation of the particles. However, for non-spherical particles and for magnetic spherical particles, it is necessary to evaluate the orientational state of the system. In order to describe the orientational state of non-spherical particles and the magnetic spherical particles, it is frequently convenient in simulations to use two different coordinate systems. These are the absolute coordinate system and the local or particle coordinate system that are fi xed at each particle body. In the mathematical treatment of the rotational motion, the absolute coordinate system is transformed in parallel so that the origin coincides with that of the particle coordinate system. In order to perform particlebased simulations, quantities in the particle coordinate system must be expressed in terms of the absolute coordinate system. In the following, therefore, we show the relationship between the quantities that are expressed in these two coordinate systems.
