- #1
Bosh
- 9
- 0
Hi,
A fundamental aspect in the Hamiltonian framework of mechanics is that the q's and p's are independent. I feel like I understand the steps in the Legendre transform from Lagrangian to Hamiltonian mechanics, but I don't see how you can go from a system where only the q's are independent (the qdots are just time derivatives of the q's) to one where both q and p are independent.
In thermodynamics Legendre transforms you always go from from sets of 2 independent quantities to other sets of 2 independent quantities. It seems to be saying that in Lagrangian mechanics q and qdot are independent, but I can't seem to make sense of that.
Any help would be appreciated!
A fundamental aspect in the Hamiltonian framework of mechanics is that the q's and p's are independent. I feel like I understand the steps in the Legendre transform from Lagrangian to Hamiltonian mechanics, but I don't see how you can go from a system where only the q's are independent (the qdots are just time derivatives of the q's) to one where both q and p are independent.
In thermodynamics Legendre transforms you always go from from sets of 2 independent quantities to other sets of 2 independent quantities. It seems to be saying that in Lagrangian mechanics q and qdot are independent, but I can't seem to make sense of that.
Any help would be appreciated!