All Questions
Tagged with classical-mechanics vector-fields
5
questions
8
votes
1
answer
702
views
Can any symplectomorphism (1 Definition of canonical transformation) be represented by the flow of a vectorfield?
For this question I will use the definition that a canonical transformation is a map $T(q,p)$ from the phase space onto itself, which leaves the symplectic 2-form invariant (which is the definition of ...
- 6,763
11
votes
2
answers
1k
views
Does Hamilton Mechanics give a general phase-space conserving flux?
Hamiltonian dynamics fulfil the Liouville's theorem, which means that one can imagine the flux of a phase space volume under a Hamiltonian theory like the flux of an ideal fluid, which doesn't change ...
- 175
2
votes
2
answers
1k
views
What are the mathematical models for force, acceleration and velocity?
In mechanics, the space can be described as a Riemann manifold. Forces, then, can be defined as vector fields of this manifold. Accelerations are linear functions of forces, so they are covector ...
- 905
1
vote
2
answers
129
views
Time derivative of unit velocity vector?
Let's say I have some parametric curve describing the evolution of a particle $\mathbf{r}(t)$. The velocity is $\mathbf{v}(t) = d\mathbf{r}/dt$ of course. I am trying to understand what the expression ...
6
votes
3
answers
2k
views
Paths in phase space can never intersect, but why can't they merge?
Page 272 of No-Nonsense Classical Mechanics sketches why paths in phase space can never intersect:
Problem: It seems to me this reasoning only implies that paths can never "strictly" ...
- 337