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We propose a planar chain system, which is a simple mechanical system with aconstraint. It is composed of $N$ masses connected by $N-1$ light links. It canbe considered as a model of a chain system, e.g., a polymer, in which each bondis replaced by a rigid link. The long time average of the kinetic energies ofthe masses in this model is numerically computed. It is found that the averagekinetic energies of the masses are different and masses near the ends of thechain have large energies. We explain that this result is not in contradictionwith the principle of equipartition. The apparent violation of equipartition isobserved not only in the planar chain systems but also in other constrainedsystems. We derive an approximate expression for the average kinetic energy,which is in qualitative agreement with the numerical results.

Apparent violation of equipartition of energy in constrained dynamical systems