Abstract: Modern differential geometry is applied as the tool of study for non-holonomic systems. Introduction of 1-form based on a manifold M-leads to the corresponding contact form and cartan form, obtaining the Boltzmann-Hamel equation of a nonholonomi c system under the differential form.At the same time,when the system is under first order linearly homogen-oeus nonholonomic cons t raint ,si mi lar Bol tzmann-Hamel equation is obtained, more close to the classic form. Finally, some applications of the equations are shown through examples.