- #1
dRic2
Gold Member
- 883
- 225
I'm reading a book about analytical mechanics and in particular, in a chapter on hamiltonian Mechanics it says:
"In the state space (...) the complete solutionbof the canonical equations is pictured as an infinite manifold of curves which fill (2n+1)-dimensional space. These curves never cross each other. Indeed, such crossing would mean that two tangents are possible at the same point of the state space , but that is excluded because of the canonical equations which give a unique tangent at any point of the space."
I'm not following very well the argument of the author. Can someone help me, please ?
Thanks
Ric
"In the state space (...) the complete solutionbof the canonical equations is pictured as an infinite manifold of curves which fill (2n+1)-dimensional space. These curves never cross each other. Indeed, such crossing would mean that two tangents are possible at the same point of the state space , but that is excluded because of the canonical equations which give a unique tangent at any point of the space."
I'm not following very well the argument of the author. Can someone help me, please ?
Thanks
Ric