Physical dynamics

Author: E.M. Lifshitz et al
Publisher:
Publish Date: 1999-05-01
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Fragment: The above arguments are, of course, general ones, and apply to any rapidly varying quantities (phases) which take values in infinite ranges. Returning to the rotational degrees of freedom of molecules, let us note that in polyatomic gases the distribution function may also depend on the angles which specify the fixed orientation of the axes of the molecules relative to the vector M. For example, in molecules of the symmetrical top type this is the precession angle between M and the axis of the top, whereas the distribution function may again be regarded as independent of the rapidly varying angles of rotation of the top about its own axis and precession of this axis about M. The vibrational motion of the atoms within the molecule is practically always quantized, so that the vibrational state of the molecule is specified by the appropriate quantum numbers. Under ordinary conditions (at not too high temperatures), however, the vibrations are not excited at all, and the molecule is at its ground vibrational level. In this chapter we shall denote by F the set of all variables on which the distribution function depends, other than the coordinates of the molecule as a whole (and the time). We separate from the phase volume element dτ the factor dV = dx dy dz, and denote by dF the remaining factor in terms of the variables used (and integrated over the angles on which f does not depend). The quantities F have an important common property: they are integrals of the motion, and remain constant for each molecule during its free motion (in the absence of an external field) between successive collisions; but they are in general altered by each collision. The coordinates x, y, z of the molecule as a whole vary, of course, during its free motion.