All Questions
7 questions
10
votes
1
answer
400
views
Rigorous treatment of Ostrogradsky's instability theorem?
The Ostrogradsky instability theorem says that if a Lagrangian depends on more than the position and velocity, the corresponding Hamiltonian is unbounded below. This has been suggested as a reason why ...
- 1,924
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
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
3
votes
0
answers
194
views
Rigid-body in a central field: orbital and attitude motion
Question
I would like to find a nice set of explicit coordinates for the family (parametrised by angular momentum) of reduced systems representing a rigid-body in a central field
in which the orbital ...
6
votes
1
answer
1k
views
How the Jacobi metrics may be useful in mechanics with or without constraints?
A mechanical system $(Q,K,V)$ is specified by the configuration space $Q,$ the potential energy $V\in C^\infty(Q),$ and the kinetic energy $K=K_g$ given by a Riemannian metric $g$ on $Q.$
If $V{<}...
- 4,306
5
votes
1
answer
628
views
What are the canonical and earliest references to trivial symmetries in gauge systems?
I am trying to find canonical references and the history of trivial symmetries.
The earliest text book reference I can find is on page 69 of Quantization of Gauge Systems by Henneaux and Teitelboim.
...
- 461
17
votes
5
answers
2k
views
2- and 3-body problems when gravity is not inverse-square
Suppose that gravity did not follow an inverse-square law, but was instead a central force diminishing
as $1/d^p$ for distance separation $d$ and some power $p$.
Two questions:
Presumably the 2-body ...
- 151k