All Questions
239
questions
3
votes
2
answers
139
views
Other infinitesimal variation of the action
I was reading this post about the virial theorem where the virial theorem comes from varying the action by the infinitesimal rescaling $x\rightarrow(1+\epsilon)x$ and asking that $\delta S=0$ under ...
- 1,168
1
vote
1
answer
152
views
Significance of Lagrangian in Principle of Least Action?
I've been studying the Legendre transform and it's been a fun realization to see that the relationship between the Lagrangian and the Hamiltonian is simply a Legendre transform, i.e.,
$$\{H, p\}\...
- 802
1
vote
2
answers
105
views
What will happen if we take up Cartesian Coordinates in Lagrangian Formulation instead of Generalized Coordinates?
Why do we actually need generalized coordinates? Is it a mathematical manipulation only or does it serve physical purpose? And will principle of stationary action stay valid if we use cartesian ...
- 132
0
votes
2
answers
85
views
Time reversal on potential $V(\frac{d^n {\vec x}( t)}{d t^n})$ with any odd or even power time-derivative on the position function
In this post, I tried to challenge what @Richard Myers said in his answer in https://physics.stackexchange.com/a/633205/42982. I followed what he said, except I kept a common widely used notation $\...
- 4,336
3
votes
2
answers
2k
views
The first and second form of Euler-(Lagrange) equation with explicit time dependence
I have learned the first and second form of Euler-(Lagrange) equation with no explicit time dependence (the time dependence only implicit on the function to be solved, say $y\left(t\right)$), from ...
- 4,336
2
votes
2
answers
284
views
Lagrange equation 1788, and Hamilton principle 1834
Lagrange's equation and Lagrangian and derived in 1788. It is different from Newtonian mechanics view because Newton emphasizes the external force acts on the body. But the Lagrange's. view is that ...
- 4,336
1
vote
1
answer
866
views
Solve the hanging rope shape using the variational principle? [duplicate]
I know how to write down the local ordinary differential equation (ODE) via Newton's force law, balancing between the left and right rope tension and the gravity exerted on a infinitesimal piece of ...
- 4,336
14
votes
6
answers
2k
views
Does universal speed limit of information contradict the ability of a particle to pick a trajectory using Principle of Least Action?
I'm doing some self reading on Lagrangian Mechanics and Special Relavivity. The following are two statements that seem to be taken as absolute fundamentals and yet I'm unable to reconcile one with the ...
user297575
1
vote
0
answers
20
views
Can we go from equations of motion back to Lagrangian? [duplicate]
We always go in one direction, from Lagrangian to equations of motion (classical mechanics). But is it possible to go the opposite way, from equation of motion to Lagrangian? Suppose we have an ...
- 2,625
1
vote
0
answers
93
views
What's special about the $T-V = H- 2V =2 T- H$, which the least action principle extremizes? [duplicate]
My question is simple.
In the classical mechanics, we know the least action principle does the variation on the action
$$
S = \int (T-V) dt ,
$$
where $T$ is the kinetic term and $V$ is the potential ...
- 4,336
3
votes
3
answers
562
views
Least action principle remark on negative mass in Landau-Lifshitz classical mechanics
In the famous Landau-Lifshitz's Classical Mechanics there is a remark I cannot fully understand at the very beginning of the book (page 7 of the second edition):
It is easy to see that mass of a ...
- 43
2
votes
2
answers
148
views
Do dynamic systems that are based on a variational principle imply a conservation law?
In many dynamic systems in classical physics, as well as quantum mechanics, the equation of motion can be derived from a variational principle (VP), i.e. minimizing an action integral of some sort.
I ...
- 261
1
vote
0
answers
48
views
Why does nature favour systems that follow from a variational principle? [closed]
When Newton discovered ‘Newton’s law’ he was probably not aware that it could be viewed as a consequence of minimizing an ‘action integral’ (integral of some Lagrangian density).
Since the same is ...
- 261
14
votes
4
answers
2k
views
Connection between different kinds of "Lagrangian"
Being a physic student I first heard the term: "Lagrangian" during a course about Lagrangian mechanics; at that time this term was defined to me in the following way:
For a classic, non ...
- 4,577
1
vote
2
answers
345
views
Jerk mechanics - Lagrangian
I have a Lagrangian with the form
$$L = L[q(t,\alpha), \dot{q}(t,\alpha), \ddot{q}(t,\alpha), t],$$
to which I am applying the calculus of variations. The problem is that when I apply the calculus, I ...
- 3,122