- #1
Radarithm
Gold Member
- 158
- 2
After studying the methods of Lagrange and Hamilton for a bit I still find myself uneasy about the action. I don't even know how to define it other than the integral of the Lagrangian with respect to time:
$$I=\int_{t_1}^{t_2}\mathrm{d}t\, L(q,\dot{q},t)$$
Does the action have any significance? I also still fail to see the connection between the action and its corresponding configuration / phase space (is it related to both?). What's really been getting to me is this: why does the action have to be a local min/max/stationary point? What if it wasn't? I'm planning to delve deeper into the topic soon (Hamilton-Jacobi, Canonical transformations, etc) but these gaps in my knowledge are quite irritating.
$$I=\int_{t_1}^{t_2}\mathrm{d}t\, L(q,\dot{q},t)$$
Does the action have any significance? I also still fail to see the connection between the action and its corresponding configuration / phase space (is it related to both?). What's really been getting to me is this: why does the action have to be a local min/max/stationary point? What if it wasn't? I'm planning to delve deeper into the topic soon (Hamilton-Jacobi, Canonical transformations, etc) but these gaps in my knowledge are quite irritating.