All Questions

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,...

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,......

Apparently one identifies the configuration space in physics often with a manifold $M$. The tangent bundle $TM$ is then the space of all possible positions and velocities. Furthermore, many sources ...

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, \...

In many courses in theoretical classical mechanics Hamiltonian formalism takes an important place. However I did not see it applied to problems of classical mechanics (unless one expands the scope of ...