All Questions
Tagged with hamiltonian-mechanics sg.symplectic-geometry
52 questions
2
votes
1
answer
609
views
Computation with the Legendre Transform
Let $M$ be a manifold and fix a Lagrangian $L\in C^\infty(T M )$. Let $x_1,\dots x_n$ be local coordinates for $M$ and equip the tangent bundle and cotangent bundle with standard coordinates $(x_1,\...
- 243
2
votes
0
answers
143
views
Is it true that a nondegenerate minimizing periodic orbit of mechanical Hamiltonian system is hyperbolic
Consider mechanical Hamiltonian system of the form
$$H(p,q)=\dfrac{\Vert p\Vert^2}{2}+V(q),\quad (q,p)\in T^*\mathbb T^n.$$
Here we suppose the periodic orbit $\gamma$ minimizes the Lagrangian ...
- 197