Bonus
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>
| Editions | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|
| 1 | 49 | 12.24 | 78% | 39% | 6% |
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| Carnegie Mellon A | Ohio State B | 10 | 10 | 0 | 20 | EM |
| Case Western B | Michigan State | 10 | 0 | 0 | 10 | E |
| Kenyon | Michigan C | 0 | 0 | 0 | 0 | |
| Michigan A | Michigan B | 10 | 10 | 0 | 20 | EM |
| Michigan D | Case Western A | 0 | 0 | 0 | 0 | |
| Ohio State A | Carnegie Mellon B | 10 | 0 | 0 | 10 | E |
Summary
| Tournament | Edition | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|
| California | 2025-02-01 | 3 | 16.67 | 100% | 33% | 33% |
| Florida | 2025-02-01 | 3 | 10.00 | 33% | 33% | 33% |
| Great Lakes | 2025-02-01 | 6 | 10.00 | 67% | 33% | 0% |
| North | 2025-02-01 | 3 | 13.33 | 100% | 33% | 0% |
| Overflow | 2025-02-01 | 5 | 10.00 | 60% | 20% | 20% |
| Pacific Northwest | 2025-02-01 | 2 | 5.00 | 50% | 0% | 0% |
| South Central | 2025-02-01 | 2 | 20.00 | 100% | 100% | 0% |
| Southeast | 2025-02-01 | 4 | 5.00 | 50% | 0% | 0% |
| UK | 2025-02-01 | 10 | 14.00 | 100% | 40% | 0% |
| Upper Mid-Atlantic | 2025-02-01 | 8 | 16.25 | 88% | 75% | 0% |
| Upstate NY | 2025-02-01 | 3 | 10.00 | 67% | 33% | 0% |