All Questions
231
questions
3
votes
1
answer
511
views
Can I find a potential function in the usual way if the central field contains $t$ in its magnitude?
I'm working on a classical mechanics problem in which the problem states that a particle of mass $m$ moves in a central field of attractive force of magnitude:
$$F(r, t) = \frac{k}{r^2}e^{-at}$$
$r$ ...
- 31
6
votes
2
answers
2k
views
What are the reasons for leaving the dissipative energy term out of the Hamiltonian when writing the Lyapunov function?
I have a problem with one of my study questions for an oral exam:
The Hamiltonian of a nonlinear mechanical system, i.e. the sum of the kinetic and potential energies, is often used as a Lyapunov ...
- 201
16
votes
3
answers
6k
views
Hamilton-Jacobi Equation
In the Hamilton-Jacobi equation, we take the partial time derivative of the action. But the action comes from integrating the Lagrangian over time, so time seems to just be a dummy variable here and ...
- 921
3
votes
1
answer
924
views
Origins of the principle of least time in classical mechanics
Is it possible to derive the principle of least time from the principle of least action in lagrangian or hamiltonian mechanics? Or is Fermat's principle more fundamental than the principle of least ...
- 1,352
96
votes
4
answers
32k
views
Physical meaning of Legendre transformation
I would like to know the physical meaning of the Legendre transformation, if there is any? I've used it in thermodynamics and classical mechanics and it seemed only a change of coordinates?
- 1,227
29
votes
9
answers
25k
views
Book about classical mechanics
I am looking for a book about "advanced" classical mechanics. By advanced I mean a book considering directly Lagrangian and Hamiltonian formulation, and also providing a firm basis in the geometrical ...