Timeline for Conservative forces and Variation
Current License: CC BY-SA 4.0
4 events
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| Dec 3, 2023 at 18:42 | comment | added | Ben H | Treating the work integral as an action, one would have $W = \int_0^1 \vec{F}\left(\vec{r}(t)\right) \cdot \frac{{\rm d}\vec{r}}{{\rm d}t}(t)\, {\rm d}t$, or $W = \int_0^1 L\left(\vec{q}, \dot{\vec{q}}\right) {\rm d}t$, with Lagrangian $L = F_i\left(\vec{q}, \dot{\vec{q}}\right) \dot{q}_i$, and where the path $\vec{q}(t) = \vec{r}(t)$ has fixed endpoints at $t=0$ and $t=1$. If the force is independent of velocity then the Euler-Lagrange equation is $\frac{{\rm d} F_i}{{\rm d} t} = \frac{\partial F_i}{\partial q_j} \dot{q}_i$. Not sure how that would be useful. | |
| Nov 10, 2023 at 15:21 | answer | added | Benjamin Feldern | timeline score: 0 | |
| Nov 10, 2023 at 13:58 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
added 2 characters in body; edited tags
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| Nov 10, 2023 at 13:10 | history | asked | Charu _Bamble | CC BY-SA 4.0 |