Starting from the equations of motion of a simple system possessing th
e properties of elastic and plastic bodies, we construct its Lagrangia
n and Hamiltonian functions and also the Rayleigh dissipation function
. This allows us to find the rate of heating of the system and to anal
yze the fluctuations of basic observables. Introducing into the Hamilt
on-Rayleigh equation of motion a random force producing on average the
same effects as a dissipation function, we arrive first at the Langev
in equations describing the fluctuations and then at a kinetic equatio
n for the distribution function defined in the space of the collective
variables. In this way a rather general scheme is established for sol
ving dynamical problems in different and more complex elastoplastic sy
stems, in nuclear physics and maybe even in physics of molecules and a
tomic clusters. In a preliminary study, the model is applied to estima
te the probability of the quasi-fission process coming from the therma
l fluctuations of the nuclear shape. (C) 1998 Elsevier Science B.V.