Question
A function named for this scientist whose inputs are q, d-S-d-q, and time-equals-d-S-d-t. For 10 points each:
[10h] Give the first namesake scientist of that nonlinear PDE, which can be solved to determine the action. This scientist’s “principle” is a statement of the principle of least action that can be written “d-S-d-q equals zero.”
ANSWER: William Rowan Hamilton (The PDE is the Hamilton–Jacobi equation.)
[10m] The action also equals the time integral of this quantity, which is named for a naturalized Frenchman and equals the difference of kinetic and potential energy.
ANSWER: Lagrangian [prompt on L]
[10e] In Hamiltonian mechanics, q is a vector of the "generalized" type of these quantities. Systems for these quantities include spherical, Cartesian, and polar.
ANSWER: coordinates [accept generalized coordinates or spherical coordinates or Cartesian coordinates or polar coordinates; accept coordinate systems]
<Science - Physics>
Data
Summary
| Tournament | Edition | Exact Match? | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|---|
| 2025 PACE NSC | 06/07/2025 | Y | 36 | 14.72 | 86% | 47% | 14% |