Realization of Holonomic Constraints and Freezing of High-frequency Degrees of Freedom In the Light of Classical Perturbation-theory .2.

As in Part I of this paper, we consider the problem of the energy exchanges between two subsystems, of which one is a system of ngr harmonic oscillators, while the other one is any dynamical system ofn degrees of freedom. Such a problem is of interest both for the realization of holonomic constraints of classical mechanics, and for the freezing of the internal degrees of freedom in molecular collisions. The results of Part I, which referred to the particular case n=1, are here extended to the more difficult case n>1. For the rate of energy transfer we find exponential estimates of Nekhoroshev's type, namely of the form exp (lambda*/lambda)1/a , where lambda is a positive real number giving the size of the involved frequencies, and lambda* anda are constants. For the particularly relevant constanta we find in generala=1/ngr however, in the particular case when the ngr frequencies are equal (collision of identical molecules), we find a=1 independently of n, as conjectured by Jeans in the year 1903.