Newtonian-Riemannian时空中的动力学(Ⅰ)

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Dynamics in Newtonian-Riemannian Spacetime(Ⅰ)

摘要: 根据现代微分几何的理论,力学原理及现代微积分把Newtonian-Galilean时空中的动力学推广到Newtonian-Riemannian时空中,建立N-R时空中的动力学,分几个部分,(Ⅰ)是其中之一,余后续。
- Ricmannian流形 /
- 连络 /
- 绝对微分 /
- Lie导数 /
- 共同运动时间导数 /
- 纤维丛 /
- 对偶对
Abstract: By the theory of Modern Geometry,the mechanical principle and advanced calculus,the dynamics in Newtonian-Galilean spacetime is generalized to Newtonian-Riemannian Spacetime,and the dynamics in N-Rspacetime is established.Beng divided into some parts,this paper is one of them.The other are to be continued.
- Riemannian manifold /
- connection /
- absolute differ ential /
- Lie derivative /
- exterior differ ential /
- co-moving time derivative /
- fiber bundle

[1]	William L Burke. Applied Differential Geometry[M]. Cambridge University Press,1985.
[2]	Bernard F Schutz. Geometrical Methods of Mathematical Physics[M]. Cambridge University Press,1980.
[3]	Curtis W D, Miller F R. Differential Manifolds and Theoretical Physics[M]. Academic Press, Inc,1985.
[4]	Von C, Westenholz. Differential Forms in Mathematical Physics[M]. North-Holland Publishing Company, 1978.
[5]	Ralph Abraham, Marsden J E, Tudor Ratiu. Manifolds Tensor Analysis and Applications[M]. Addison-wesley Publishing Company,1983.