Abstract:
In some previous articles, we defined several partitions of the total
kinetic energy $T$ of a system of $N$ classical particles in ${\mathbb R}^d$ into
components corresponding to various modes of motion. In the present paper,
we propose formulas for the mean values of these components in the
normalization $T=1$ (for any $d$ and $N$) under the assumption that the
masses of all the particles are equal. These formulas are proven at the
“physical level” of rigor and numerically confirmed for planar systems
($d=2$) at $3\leqslant N\leqslant 100$. The case where the masses of the particles
are chosen at random is also considered. The paper complements our article
of 2008 [Russian J. Phys. Chem. B, 2(6):947–963] where similar numerical
experiments were carried out for spatial systems ($d=3$) at $3\leqslant N\leqslant
100$.
Keywords:multidimensional systems of classical particles, instantaneous phase-space invariants, kinetic energy partitions, formulas for the mean values, hyperangular momenta.
References