| 非完整系统Boltzmann—Hamel方程的几何理论 |
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| 引用本文： | 唐传龙,史荣昌.非完整系统Boltzmann—Hamel方程的几何理论[J].北京理工大学学报,1989,9(1):35-43. |
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| 作者姓名： | 唐传龙 史荣昌 |
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| 作者单位： | 北京理工大学应用力学系
(唐传龙)，北京理工大学应用数学系(史荣昌) |
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| 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。
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| 关 键 词： | 分析力学 非完整系统 微分几何 |
GEOMETRIC THEORY OF THE BOLTZMANN-HAMEL EQUATION OF NONHOLONOMIC SYSTEMS |
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| Tang Chuanlong.GEOMETRIC THEORY OF THE BOLTZMANN-HAMEL EQUATION OF NONHOLONOMIC SYSTEMS[J].Journal of Beijing Institute of Technology(Natural Science Edition),1989,9(1):35-43. |
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| Authors: | Tang Chuanlong |
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| Institution: | Tang Chuanlong(Department of Applied Mechanics)Shi Rongchang (Department of Applied Mathematics) |
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| 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. |
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| Keywords: | analytic mechanics nonholonomic system differential geometry the Bol tzmann-Hamel equation |
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