a nonholonomic mechanical structure for the two-dimensional monolayer systems

In this paper we study the dynamics of the 2dmotion of a particle of monolayer . first we consider the usual physical time component and the plan manifold r2, having the polar coordinates. then a geometric approach to nonholonomic constrained mechanical systems is applied to a problem from the two dimensional geometric dynamics of the langmuirblodgett monolayer . we consider a constraint submanifold of the 1jet space j1(t, r2),corresponding to the given constraint condition in a monolayer space and construct the corresponding constrained mechanical system on the constraint submanifold . so the equation of motion defined on the constraint submanifold is presented.