- #1
Simfish
Gold Member
- 823
- 2
It's given as this
[tex]H\left(q_i,p_j,t\right) = \sum_m \dot{q}_m p_m - L(q_i,\dot q_j(q_h, p_k),t) \,.[/tex]
But if it's a Legendre transformation, then couldn't you also do this?
[tex]H\left(q_i,p_j,t\right) = \sum_m \dot{p}_m q_m - L(p_i,\dot p_j(p_h, q_k),t) \,.[/tex]
[tex]H\left(q_i,p_j,t\right) = \sum_m \dot{q}_m p_m - L(q_i,\dot q_j(q_h, p_k),t) \,.[/tex]
But if it's a Legendre transformation, then couldn't you also do this?
[tex]H\left(q_i,p_j,t\right) = \sum_m \dot{p}_m q_m - L(p_i,\dot p_j(p_h, q_k),t) \,.[/tex]