Timeline for Are these two expressions for $\mathrm{d}E/\mathrm{d}t$ compatible?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 12, 2021 at 20:41 | answer | added | Eli | timeline score: 3 | |
| Apr 11, 2021 at 20:13 | answer | added | Qmechanic♦ | timeline score: 4 | |
| Apr 11, 2021 at 17:53 | comment | added | Pablo T. | Indeed, @Eli, in that example $V=-mgL\cos(\Omega t - \theta)$ there is no dependence on the generalised velocities, hence it is a conservative potential and $V_0=V$, $V_1 = 0$. | |
| Apr 11, 2021 at 17:37 | comment | added | Eli | the potential energy id not depending on the velocity i gave you example pendulum | |
| Apr 11, 2021 at 17:31 | history | edited | Pablo T. | CC BY-SA 4.0 |
added 20 characters in body
|
| Apr 11, 2021 at 17:30 | comment | added | Pablo T. | @Eli $V_0$ and $V_1$ are homogeneous polynomials of degree $0$ and $1$ on the generalised velocities. As a conservative $V$ only depends on $q^k,t$ and not in $\dot{q}^k$, it equals its own $V_0$, and $V_1 = 0$. | |
| Apr 11, 2021 at 17:17 | comment | added | Eli | lets take pendulum that rotate ,the potential energy is $~V=-m\,g\,L\cos(\Omega\,t-\theta)~$ hence the time is not explicit you can't obtain $~V=V_0+V_1$ or what is your $V_0$ and $V_1$ in this case ? | |
| Apr 11, 2021 at 17:07 | history | edited | Pablo T. | CC BY-SA 4.0 |
small edits made, inspired by a comment, to make the post slightly easier to understand.
|
| Apr 11, 2021 at 17:05 | comment | added | Pablo T. | By $V$, @Eli, I meant a generalised potential, which can depend on the $\dot{q}$s. But, considering that's not relevant for my question, maybe I should've just assumed $V$ is a conservative potential $V(q,t)$ all along (it can still depend on $t$, tho). | |
| Apr 11, 2021 at 14:35 | comment | added | Eli | "We would do the same for V" ?. V is not depending on the velocity and not explicit depending on the time. hence you can split it to $V_0+V_1+V_2$ | |
| Apr 10, 2021 at 17:05 | history | edited | Pablo T. | CC BY-SA 4.0 |
edited body
|
| Apr 10, 2021 at 16:48 | history | edited | Pablo T. | CC BY-SA 4.0 |
added 7 characters in body
|
| Apr 10, 2021 at 16:29 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
edited tags
|
| Apr 10, 2021 at 16:23 | history | asked | Pablo T. | CC BY-SA 4.0 |