Question
The partial derivatives of this quantity with respect to q and q-dot appear in a second-order PDE co-named for Euler. For 10 points each:
[10e] Name this quantity defined as kinetic energy minus potential energy, which is used in a formulation of classical mechanics contrasted with Hamiltonian mechanics.
ANSWER: Lagrangian [accept Lagrangian mechanics]
[10m] The variable q in the definition of the Lagrangian is a generalized one of these quantities. These quantities are called “cyclic” or “ignorable” if they correspond to a constant of motion.
ANSWER: coordinates [accept generalized coordinates or cyclic coordinates]
[10h] In a system with cyclic coordinates, the equations of motion can be solved using a method named for this physicist, which defines a new quantity from the Lagrangian and Hamiltonian. With Hurwitz, this physicist names a stability criterion for control systems.
ANSWER: Edward Routh (“rao’th”) [or Edward John Routh; accept Routh’s method or Routhian mechanics; accept Routh–Hurwitz criterion]
<Virginia Tech A, Physics>
Summary
| California | 2025-02-01 | Y | 3 | 16.67 | 100% | 33% | 33% |
| Florida | 2025-02-01 | Y | 3 | 10.00 | 33% | 33% | 33% |
| Great Lakes | 2025-02-01 | Y | 6 | 10.00 | 67% | 33% | 0% |
| North | 2025-02-01 | Y | 3 | 13.33 | 100% | 33% | 0% |
| Overflow | 2025-02-01 | Y | 5 | 10.00 | 60% | 20% | 20% |
| Pacific Northwest | 2025-02-01 | Y | 2 | 5.00 | 50% | 0% | 0% |
| South Central | 2025-02-01 | Y | 2 | 20.00 | 100% | 100% | 0% |
| Southeast | 2025-02-01 | Y | 4 | 5.00 | 50% | 0% | 0% |
| UK | 2025-02-01 | Y | 10 | 14.00 | 100% | 40% | 0% |
| Upper Mid-Atlantic | 2025-02-01 | Y | 8 | 16.25 | 88% | 75% | 0% |
| Upstate NY | 2025-02-01 | Y | 3 | 10.00 | 67% | 33% | 0% |
Data
| Georgia Tech D | Alabama A | 10 | 0 | 0 | 10 |
| Georgia Tech A | Georgia Tech B | 0 | 0 | 0 | 0 |
| Louisville A | Tennessee A | 0 | 0 | 0 | 0 |
| Bruin A | Georgia Tech C | 10 | 0 | 0 | 10 |