All Questions
5
questions
10
votes
3
answers
4k
views
Is there a valid Lagrangian formulation for all classical systems?
Can one use the Lagrangian formalism for all classical systems, i.e. systems with a set of trajectories $\vec{x}_i(t)$ describing paths?
On the wikipedia page of Lagrangian mechanics, there is an ...
- 8,523
19
votes
1
answer
1k
views
Why are Hamiltonian Mechanics well-defined?
I have encountered a problem while re-reading the formalism of Hamiltonian mechanics, and it lies in a very simple remark.
Indeed, if I am not mistaken, when we want to do mechanics using the ...
- 2,296
25
votes
3
answers
29k
views
Constructing Lagrangian from the Hamiltonian
Given the Lagrangian $L$ for a system, we can construct the Hamiltonian $H$ using the definition $H=\sum\limits_{i}p_i\dot{q}_i-L$ where $p_i=\frac{\partial L}{\partial \dot{q}_i}$. Therefore, to ...
- 26.8k
2
votes
1
answer
1k
views
Difference between the energy and the Hamiltonian in a specific example
The problem is the following:
Consider a particle of mass $m$ confined in a long and thin hollow pipe, which rotates in the $xy$ plane with constant angular velocity $\omega$. The rotation axis ...
- 1,045
8
votes
5
answers
716
views
Why can't we obtain a Hamiltonian from the Lagrangian by only substituting?
This question may sound a bit dumb. Why can't we obtain the Hamiltonian of a system simply by finding $\dot{q}$ in terms of $p$ and then evaluating the Lagrangian with $\dot{q} = \dot{q}(p)$? Wouldn't ...
- 590