Rotational Brownian Motion of an Asymmetric Top, Phys. Rev. Al9

Some time ago J.T. Lewis, J. McConnell and I published a paper with this same title in which we showed how methods of stochastic differential equations could be used to discuss the motion of an asymmetric top driven by white noise random torques [1]. Since the detailed results, including the application to the calculation of complex polarizabilities of asymmetric top molecules and the cor-relation times associated with the dipolar broadening of nuclear magnetic resonance lines, are given in that paper, I will not give them here and will instead emphasize the general methods. In part these methods are those described in a set of unpublished “Notes on Stochastic Differential Equations ” which I wrote in June 1974, inspired by a visit and talk at the University of Michigan by N.G. van Kampen. In his talk van Kampen described the methods based on the cumulant expansion of the time-ordered exponential which he and, independently, R.F. Fox had developed for handling multiplicative stochastic equations [2, 3]. I realized that the same results could be obtained by an extension of the Method of Averaging of Krylov and Bogoliubov [4,5], a well known method of nonlinear mechanics, and that is what is described in the above mentioned notes. The averaging method applies to nonlinear as well as to linear stochastic differential equations and the application to rotational Brownian motion is in part an illustration of this advantage