Timeline for Boundary conditions for calculus of variations in phase space and under canonical transformations
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Oct 23, 2023 at 9:32 | history | edited | dennismoore94 | CC BY-SA 4.0 |
replaced "orbital" with "path"
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| Oct 2, 2018 at 5:47 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
Tried to make the title more descriptive
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| Oct 1, 2018 at 21:48 | vote | accept | dennismoore94 | ||
| Sep 30, 2018 at 22:45 | comment | added | dennismoore94 | OK, I think this is, what I actually don't understand: here $\delta p(t_1)=\delta p(t_2)=0$ is the same as $\delta \dot{q}(t_1)=\delta \dot{q}(t_2)=0$ would be in Lagrangian mechanics (again, thinking in cartesian coordinates), but in Lagrangian mechanics we don't have this kind of condition for the velocity. Or do we? | |
| Sep 30, 2018 at 22:15 | comment | added | Trevor Kafka | I think you're confusing $\delta p$ and $p$. We're varying both $q$ and $p$ when we work in a variational principle but hold both $q$ and $p$ fixed at the endpoints of the path. $\delta q = \delta p = 0$ at the endpoints, even if the values of $q$ and $p$ are nonzero themselves. | |
| Sep 30, 2018 at 22:12 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
added 12 characters in body; edited tags
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| Sep 30, 2018 at 22:11 | answer | added | Qmechanic♦ | timeline score: 5 | |
| Sep 30, 2018 at 21:54 | comment | added | dennismoore94 | Endpoints are fixed indeed ($\delta q(t_1)=\delta q(t_2)=0$), but for some function $f(\boldsymbol{q,p})$, $\delta f(\boldsymbol{q,p})=0$ would require $\delta p(t_1)=\delta p(t_2)=0$ too and I can't see how fixing the endpoints only (and not the derivatives!) guarantees this condition. | |
| Sep 30, 2018 at 20:56 | comment | added | Trevor Kafka | Endpoints are held fixed during the path variation, so the variation of any function at the endpoints is zero. | |
| Sep 30, 2018 at 20:40 | history | edited | dennismoore94 | CC BY-SA 4.0 |
edited title
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| Sep 30, 2018 at 16:33 | history | asked | dennismoore94 | CC BY-SA 4.0 |