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关于Kahler流形上的Newton力学 被引量:3

Newtonian Mechanics on Kahler Manifold
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摘要 本文讨论Kahler流形上的Newton力学.在此给出Newton定律、动能定律、动量定律、虚位移原理、D'Alembert-Lagrange原理、运动方程及“普遍运动方程”等的复的数学形式. In this paper we discuss Newtonian Mechanics on Kahler Manifold, and also give the complex mathematical aspects of Newton 's law, the law of kinetic energy,the law of kinetic quantity, the equation of motion and the 'general equation of dynamics'. and so on.
作者 张荣业
出处 《应用数学和力学》 CSCD 北大核心 1996年第8期709-719,共11页 Applied Mathematics and Mechanics
关键词 对偶对 牛顿定律 KAEHLER流形 牛顿力学 Kahler Manifold, a connection, an absolute differential, the dualitypairing
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参考文献2

  • 1陈省身,微分几何讲义,1983年
  • 2甘特马赫 K R,分析力学讲义,1963年

同被引文献19

  • 1干特马赫尔ФР 钟奉俄 薛问西 译.分析力学[M].北京:人民教育出版社,1963.1-163.
  • 2Arnold V I.Mathematical Methods of Classical Mechanics[M].New York:Springer-Verlag,1978,1-300.
  • 3Arnold V I.Mathematical Aspect of Classical and Celestial Mechanics.Encyclopaedia of Mathematical Sciences,Vol3.Dynamical Systems3[M].New York:Springer-Verlag,1985,1-48.
  • 4Curtis W D,Miller F R.Differential Manifolds and Theoretial Physics[M].Orlando,Florida:Academic Press Inc,1985,1-191.
  • 5Dubrorin B A,Fomenko A T,Novikov S P.Modern Geometry-Methods and Application[M].Parts Ⅰ,Parts Ⅱ.New York:Springer-Verlag,New York Inc,1984,1-374,1-357.
  • 6von Westenholz C.Differential Forms in Mathematical Physics[M].Amsterdam,New York,Oxford:North-Holland Publishing Company,1978,335-439.
  • 7Arnold V I. Mathematical Aspect of Clasical and Celestial Mechanics. Encyclopaedia of Mathematical Sciences, Vol3. Dynamical Systems3[ M]. New York: Springer-Verlag, 1985,1-48.
  • 8Curtis W D, Miller F R. Differential Manifolds and Theoretical Physics [ M]. Orlando, Florida: Academic Press Inc, 1985,1-191.
  • 9Dubrorin B A, Fomenko A T, Novikov S P. Modern Geometry-Methods and Application. Parts Ⅰ , Ⅱ[ M]. New York: Springer-Verlag, New York Inc, 1984,1-374,1-357.
  • 10von Westenholz C. Differential Forms in Mathematical Physics [ M]. Amsterdam, New York, Ox ford: North-Holland Publishing Company, 1978,335-439.

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