Rotational Brownian motion in an external potential field: A method based on the Langevin equation

A set of linear difference-differential equations for moments (averaged spherical harmonics) is derived through averaging of a nonlinear Euler-Langevin equation governing inertialess rotational motion of a polar particle in an external potential field without recourse to the Fokker-Planck equation. Thus, it has become possible to eliminate a labour-consuming step from theoretical calculations, namely, derivation of the Fokker-Planck equation from the Langevin equation and its subsequent solution. Several examples are considered.