A newtonian system mathematically always a trivial bundle?

  • Thread starter pellman
  • Start date
  • #1
684
5
The phase space of a Newtonian system is a cotangent bundle, where the base space is the manifold M of the configuration space (the positions) and the typical fiber is the cotangent space T*M (the momenta). Is it always the case that this cotangent bundle is the trivial bundle M x TM?
 

Answers and Replies

  • #2
1,772
127
No. The cotangent bundle is homeomorphic to the tangent bundle and tangent bundles are not always trivial. M cross TM is the manifold cross the tangent bundle, which is not what you want to say there.
 
  • Like
Likes pellman

Related Threads on A newtonian system mathematically always a trivial bundle?

  • Last Post
Replies
16
Views
1K
  • Last Post
18
Replies
514
Views
53K
  • Last Post
Replies
14
Views
5K
  • Last Post
Replies
5
Views
2K
Replies
4
Views
690
Replies
1
Views
2K
  • Last Post
Replies
0
Views
664
  • Last Post
Replies
12
Views
3K
  • Last Post
Replies
10
Views
4K
Top