# Linked Questions

3 votes
2 answers
93 views

### Why are you allowed to omit the $V^2$ term in the non-inertial frame?

I'm trying to find trying to find the Lagrangian and Hamiltonian for a particle in a non-inertial frame, but when I try to do so, I always get a quadratic term, which textbooks like Landau & ...
17 votes
1 answer
3k views

### On a trick to derive the Noether current

Suppose, in whatever dimension and theory, the action $S$ is invariant for a global symmetry with a continuous parameter $\epsilon$. The trick to get the Noether current consists in making the ...
0 votes
2 answers
142 views

7 votes
1 answer
1k views

### What variables does the action $S$ depend on?

Action is defined as, $$S ~=~ \int L(q, q', t) dt,$$ but my question is what variables does $S$ depend on? Is $S = S(q, t)$ or $S = S(q, q', t)$ where $q' := \frac{dq}{dt}$? In Wikipedia I've ...
1 vote
1 answer
1k views

2 votes
3 answers
1k views

### Is the path of stationary action unique? What are the physical implications of $L_{\dot{x}}=L_x$

Below, for any function $Q$ the notation $Q_x$ means $\frac{\partial Q}{\partial x}$, and $Q_{xx}$ means $\frac{\partial^2 Q}{\partial x^2}$. In physics, the trajectory of a particle is given by the ...