Algebraic structure and Poisson method for a weakly nonholonomic system

The algebraic structure and the Poisson method for a weakly nonholonomic system are studied. The differential equations of motion of the system can be written in a contravariant algebra form and its algebraic structure is discussed. The Poisson theory for the systems which possess Lie algebra structure is generalized to the weakly nonholonomic system. An example is given to illustrate the application of the result.