Question
Two answers required. One of these two equivalent principles directly generalizes Hertz’s principle of least curvature, while the other directly generalizes the principle of virtual work to dynamical systems. For 10 points each:
[10h] Name these equivalent principles. One gives that systems minimize a mass-weighted sum of squares of differences in acceleration, and the other gives that a sum of dot products with virtual displacement equals zero.
ANSWER: Gauss’s principle of least constraint AND D’Alembert’s principle [accept Lagrange–d’Alembert’s principle in place of “D’Alembert’s principle”]
[10m] Gauss’s principle is an example of one of these statements that give an inequality between a known quantity and and a function of a trial quantity, allowing the trial quantity to be refined by finding the extrema of a functional.
ANSWER: variational principles
[10e] Another variational principle gives that this quantity, the time integral of the Lagrangian, is minimized along a system’s true trajectory.
ANSWER: action [accept principle of least action or stationary-action principle]
<Geoffrey Wu, Physics>
Summary
| 2023 Chicago Open | 08/05/2023 | Y | 2 | 20.00 | 100% | 100% | 0% |
Data
| The Plague (anime)" was redirected to: "Oran High School Host Club | BHSU | 0 | 10 | 10 | 20 |
| Curse you, Periplus the Platypus! | Romanos IV Diogenes’ Macaroni Grill | 0 | 10 | 10 | 20 |