Timeline for In the context of field-theoretic classical Lagrangian mechanics, can we choose the Lagrange multipliers to be time-independent? - from Physics SE
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| Aug 31, 2022 at 3:25 | comment | added | Michael Engelhardt | If the constraint has to be enforced independently on every time slice $t$, the corresponding Lagrange multipliers $\Psi (t)$ must all be independent of one another. So, you cannot assume any relationship between them, in particular, you can't assume that $\Psi $ is constant in time. Maybe it would help if you reduced the clutter and just examined your question on a maximally simple mechanical example. | |
| Aug 30, 2022 at 16:25 | comment | added | Nawaf Bou-Rabee | @LSpice the OP seems to be asking about mathematical properties of the critical point of the constrained action; at least that’s how I read the question. In particular, if the critical point has the property that the Lagrange multiplier component is time independent. | |
| Aug 30, 2022 at 16:22 | comment | added | Nawaf Bou-Rabee | Why don’t you impose the constraint directly by eliminating $T_{ij}$ in the action? | |
| Aug 30, 2022 at 16:07 | comment | added | LSpice | It seems to me that your question is more about the physical than the mathematical validity of the assumption, and so not really appropriate for MO. You can always add an assumption to a mathematical model; the non-mathematical question is whether it's physically meaningful. Or am I missing the point, and you are asking whether there is something about the assumptions that forces $\frac{\partial\Psi_{i j}}{\partial t}$ to equal $0$? | |
| Aug 30, 2022 at 15:52 | history | asked | Isaac | CC BY-SA 4.0 |