This thesis study motion of a class of non-holonomic systems using geometric mechanics, that provide us an efficient way to formulate and analyze the dynamics and their temporal evolution on the configuration manifold. The kinematics equations of the system, viewed as a rigid body, are constrained by the requirement that the system maintain contact with the surface. They describe the constrained translation of the point of contact on the surface. In this thesis, we have considered three different examples with nonholonomic constraint i-e knife edge of pizza cutter, a circular disk rolling without slipping, and rolling sphere. For each example, the kinematics equations of the system are defined without the use of local coordinates, such that the model is globally defined on the manifold without singularities or ambiguities. Simulation results are included that show effectiveness of the proposed control laws.