Question
Hamilton’s principle states that systems will take a path in configuration space where this quantity remains constant, thus expressing the principle of stationary [this quantity]. For 10 points each:
[10m] Name this quantity that equals the time integral of the Lagrangian.
ANSWER: action [accept principle of stationary action; prompt on S]
[10e] Stationary points of an action functional are the solutions to equations named for Joseph-Louis Lagrange and this mathematician. His namesake number e is approximately equal to 2.718.
ANSWER: Leonhard Euler (“OY-lur”) [accept Euler–Lagrange equations or Euler’s number]
[10h] The principle of stationary action is generalized by this formalism, which attempts to find the propagator by summing the functional “e to the action times i over h-bar” over all trajectories.
ANSWER: path integral formulation
<Physics>
Summary
| 2024 ACF Winter at UC Berkeley | 2024-11-16 | Y | 3 | 20.00 | 100% | 67% | 33% |
| 2024 ACF Winter at Clemson | 2024-11-16 | Y | 6 | 18.33 | 100% | 67% | 17% |
| 2024 ACF Winter at Clemson | 2024-11-16 | Y | 6 | 18.33 | 83% | 33% | 67% |
| 2024 ACF Winter at Lehigh | 2024-11-16 | Y | 7 | 17.14 | 100% | 43% | 29% |
| 2024 ACF Winter at Northwestern | 2024-11-16 | Y | 8 | 17.50 | 100% | 63% | 13% |
| 2024 ACF Winter at Online | 2024-11-16 | Y | 7 | 10.00 | 100% | 0% | 0% |
| 2024 ACF Winter at Online | 2024-11-16 | Y | 3 | 10.00 | 67% | 0% | 33% |
| 2024 ACF Winter at Central Florida | 2024-11-16 | Y | 4 | 22.50 | 100% | 75% | 50% |
| 2024 ACF Winter at Oxford | 2024-11-16 | Y | 8 | 21.25 | 100% | 100% | 13% |
Data
| Imperial A | Bristol A | 10 | 10 | 0 | 20 |
| Cambridge A | Cambridge B | 10 | 10 | 0 | 20 |
| Oxford A | Cambridge C | 10 | 10 | 10 | 30 |
| Birmingham | Cambridge D | 10 | 10 | 0 | 20 |
| LSE B | Edinburgh | 10 | 10 | 0 | 20 |
| Imperial B | Southampton B | 10 | 10 | 0 | 20 |
| Manchester | LSE A | 10 | 10 | 0 | 20 |
| Oxford B | Warwick A | 10 | 10 | 0 | 20 |