ZHANG Rong-ye. Dynamics in Newtonian-Riemannian Space-Time(Ⅳ)[J]. Applied Mathematics and Mechanics, 2001, 22(4): 393-403.
Citation:
ZHANG Rong-ye. Dynamics in Newtonian-Riemannian Space-Time(Ⅳ)[J]. Applied Mathematics and Mechanics, 2001, 22(4): 393-403.
ZHANG Rong-ye. Dynamics in Newtonian-Riemannian Space-Time(Ⅳ)[J]. Applied Mathematics and Mechanics, 2001, 22(4): 393-403.
Citation:
ZHANG Rong-ye. Dynamics in Newtonian-Riemannian Space-Time(Ⅳ)[J]. Applied Mathematics and Mechanics, 2001, 22(4): 393-403.
Dynamics in Newtonian-Riemannian Space-Time(Ⅳ)
Received Date: 1998-09-06
Rev Recd Date:
2000-09-11
Publish Date:
2001-04-15
Abstract
Lagrangian mechanics in Newtonian-Riemannian space-time and relationship between Lagrangian mechanics and Newtonian mechanics,and between Lagrangian mechanics and Hamiltonian mechanics in N-R space-time are discussed.
Keywords:
Riemannian manifold ,
tangent bundle ,
cotangent bundle ,
fiber bundle ,
fiber ,
vector field ,
form field ,
exterior differential ,
absolute differential ,
Lie derivative ,
functional ,
variation
References
[1]
Curtis W D, Miller F R. Differential Manifolds and Theoretical Physcis[M]. Orlando,Florida: Academic Press,Inc,1985.
[2]
Arnold V I. Mathematical Methods of Classical Mechanics[M]. New York: Springer-Verlag,1978.
[3]
von Westenhoz C. Differential Forms in Mathematical Physics[M]. Amsterdam, New York,Oxford: North-Holland Publishing Company,1978.
[4]
Schutz B F. Geometrical Methods of Mathematical Physics[M]. Bath,Cambridge: Cambridge University Press,1980.
[5]
Burke W L. Applied Differential Geometry[M]. New York: Cambridge University Press,1985.
Proportional views