摘要
本文用现代微分几何的方法研究非完整系统,通过适当引入流形M上的1-形式基,导出相应的接触形式和Cartan形式,由此得到非完整系统在微分形式下的Boltzmann-Hamel方程。同时还讨论了在系统为一阶线性齐次非完整约束时,可得出与经典形式更相近的Boltzmann-Hamel方程。最后举例说明方程的应用。
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.
出处
《北京理工大学学报》
EI
CAS
CSCD
1989年第1期35-43,共9页
Transactions of Beijing Institute of Technology
基金
北京工业学院科研基金资助
关键词
分析力学
非完整系统
微分几何
analytic mechanics, nonholonomic system, differential geometry, the Bol tzmann-Hamel equation.
