- #1
aliens123
- 75
- 5
Suppose I had a Lagrangian
$$L = q+ \dot{q}^2 + t.$$
This has explicit time dependence. Now consider another Lagrangian:
$$L = q+ \dot{q}^2 .$$
Which has no explicit time dependence. But after solving for the equations of motion, I get $$\dot{q} = t/2 + C.$$
So I could now write my Lagrangian as:
$$L = q+ (t/2 + C)^2 .$$
Now it has explicit time dependence.
$$L = q+ \dot{q}^2 + t.$$
This has explicit time dependence. Now consider another Lagrangian:
$$L = q+ \dot{q}^2 .$$
Which has no explicit time dependence. But after solving for the equations of motion, I get $$\dot{q} = t/2 + C.$$
So I could now write my Lagrangian as:
$$L = q+ (t/2 + C)^2 .$$
Now it has explicit time dependence.