A Nonholonomic Mechanical Structure for the Two- Dimensional Monolayer Systems

In this paper we study the dynamics of the 2D-motion of a particle of monolayer . 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 ( 𝑅 ), corresponding to the given constraint condition in a monolayer space and construct the corresponding constrained mechanical system on the constraint submanifold . Then the equation of motion defined on the constraint submanifold is presented.