Timeline for Mechanical systems with their configuration space being a Lie group
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 25, 2021 at 11:08 | answer | added | Phil Harmsworth | timeline score: 2 | |
| May 23, 2021 at 19:18 | answer | added | Tobias Diez | timeline score: 2 | |
| May 22, 2021 at 18:11 | comment | added | Mark Grant | Well, there may also be planar revolute joints parameterized by $S^1$, but I take your point. | |
| May 22, 2021 at 18:10 | comment | added | alvarezpaiva | It's not just invariant Hamiltonian that are interesting in this context. You can also have collective Hamiltonians: if $\mu : T^* G \rightarrow \mathcal{G}^*$ is the momentum map and $h$ is a function in $\mathcal{G}^*$, you can consider the Hamiltonian $H := h \circ \mu$. This is used to model a few mechanical systems that are not quite as symmetric as those that are $G$-invariant, but still "smell" of symmetry. In that context I've seen other groups used. Check out the paper sciencedirect.com/science/article/abs/pii/0003491680901554 | |
| May 22, 2021 at 15:25 | comment | added | marmistrz | Yes, but it has the configuration space $SO(3)^k$, so it's still essentially the same. | |
| May 22, 2021 at 14:24 | answer | added | Michael Engelhardt | timeline score: 3 | |
| May 22, 2021 at 12:01 | comment | added | Mark Grant | Do things like robotic arms count as naturally occurring for you? | |
| May 22, 2021 at 10:45 | history | asked | marmistrz | CC BY-SA 4.0 |