Timeline for Lagrange's equations: What is $\dot{q}_j$?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 19, 2011 at 8:58 | vote | accept | Kit | ||
| Jul 19, 2011 at 8:27 | comment | added | Marek | More generally, consider an arbitrary curved surface in 3D. This has no symmetry at all. But you can still introduce a coordinate chart on it (think e.g. about lattitude and longitude for Earth's surface). Again, for every point on the surface you have an unique pair of numbers that describe it. | |
| Jul 19, 2011 at 8:23 | comment | added | Marek | @Kit: no, that is actually a complete opposite of the correct picture. As you vary $\mathbf r$, $q_j$s have to vary as well (otherwise they would not be good parameters). Consider a particle constrained to an unit circle. Its position is ${\mathbf r} = (x,y) = (\cos \phi, \sin \phi)$. You can see that as you vary $\mathbf r$ (respecting the constraint) the $\phi$ changes too. | |
| Jul 19, 2011 at 8:09 | comment | added | Kit | A generalized parameter $q_j$ (or $\dot{q}_j$ for that matter) is something that remains constant with respect to the particle whatever changes are made to $\mathbf{r}$ (the particle's radius vector with respect to some arbitrary origin). The usefulness of $q_j$ is that it is symmetrical wherever the particle is (or more formally, whatever $\mathbf{r}$ is). Am I correct in my understanding? | |
| Jul 19, 2011 at 7:07 | history | answered | Marek | CC BY-SA 3.0 |