All Questions
Tagged with classical-mechanics mp.mathematical-physics
12 questions
25
votes
5
answers
8k
views
Can the equation of motion with friction be written as Euler-Lagrange equation, and does it have a quantum version?
My (non-expert) impression is that many physically important equations of motion can be obtained as Euler-Lagrange equations. For example in quantum fields theories and in quantum mechanics quantum ...
- 21.8k
19
votes
3
answers
3k
views
Applications of symplectic geometry to classical mechanics
It is claimed that classical mechanics motivates introduction of symplectic manifolds. This is due to the theorem that the Hamiltonian flow preserves the symplectic form on the phase space.
I am ...
- 21.8k
34
votes
6
answers
5k
views
Is symplectic reduction interesting from a physical point of view?
Do you think that symplectic reduction (Marsden Weinstein reduction) is interesting from a physical point of view? If so, why? Does it give you some new physical insights?
There are some possible ...
- 1,222
27
votes
4
answers
13k
views
Hamiltonian, Lagrangian and Newton formalism of mechanics
If my thinking is wrong please let me know. I have little knowledge on beyond-college physics.
For research purposes, I read a few introductions to these three formalisms of classical mechanics [1,2,...
- 8,071
19
votes
3
answers
6k
views
Classical limit of quantum mechanics
There is a well-known principle that one can recover classical mechanics from quantum mechanics in the limit as $\hbar$ goes to zero. I am looking for the strongest statement one can make concerning ...
- 433
18
votes
2
answers
1k
views
Example of ODE not equivalent to Euler-Lagrange equation
I am looking for an explicit (preferably simple) example of an ODE with time-independent coefficients in $\mathbb{R}^3$ such that there does not exist an Euler-Lagrange equation
$$\frac{\partial L}{\...
- 21.8k
9
votes
1
answer
728
views
When does a Lagrangian dynamical system have an equivalent Hamiltonian description?
Let a Lagrangian dynamical system with $n$ degrees of freedom and configuration space $\mathbb{R}^n$
(i.e. phase space $\mathbb{R}^{2n}$), which is described by $L=L(q_{i},\dot{q}_{i},t)$, $i=1,2,......
- 7,746
8
votes
3
answers
5k
views
Bertrand theorem - central forces
Here is a version of Bertrand theorem. Let us consider a force $F(r)$ which depends only on the distance to a given point. If all trajectories which remain bounded are closed, then either $F(r)=ar$ ...
- 551
7
votes
2
answers
2k
views
Practical example of Hamiltonian reduction
I know what is the Liouville integrability: given a Hamiltonian with $n$ degrees of freedom, with $n$ independent constants of motion in involution, the Hamiltonian can be brought to the form $H(p_1, \...
- 469
7
votes
0
answers
479
views
Question about theorem in Arnold's book on action-angles variables
I have a question about the action-angle theorem on p. 283 in Arnold's textbook on classical mechanics.(I added the link to this book in the last part of this question)
If you don't have the book or ...
- 259
4
votes
2
answers
592
views
Can one obtain this ODE as an Euler-Lagrange equation?
Some of the second order ODE can be considered as Euler-Lagrange equations for an appropriate Lagrangian. However this is true not for arbitrary second order equation. But some of important equations ...
- 53
2
votes
0
answers
141
views
Formulation of contour variational problem
I am having difficulty formulating a problem, which involves optimizing a contour shape, into a well-posed variational form that would give a reasonable answer.
Within a bounded region on the $xy$ ...
- 183