Mechanical behaviour of motion for the two-dimensional monolayer system‎

‎In this paper we study the dynamics of the 2D-motion 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 Langmuir-Blodgett monolayer‎. We consider a constraint submanifold of the 1-jet 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.