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
| UC Berkeley A | Claremont A | 10 | 10 | 0 | 20 |
| Claremont B | UCSD | 10 | 0 | 0 | 10 |
| UCLA | UC Berkeley B | 10 | 0 | 10 | 20 |
| Michigan A | Michigan B | 10 | 10 | 0 | 20 |
| Kenyon | Michigan C | 0 | 0 | 0 | 0 |
| Michigan D | Case Western A | 0 | 0 | 0 | 0 |
| Case Western B | Michigan State | 10 | 0 | 0 | 10 |
| Ohio State A | Carnegie Mellon B | 10 | 0 | 0 | 10 |
| Carnegie Mellon A | Ohio State B | 10 | 10 | 0 | 20 |
| Florida A | Florida B | 10 | 10 | 10 | 30 |
| UCF C | Florida State A | 0 | 0 | 0 | 0 |
| Valencia A | UCF B | 0 | 0 | 0 | 0 |
| Iowa State | Wisconsin A | 10 | 10 | 0 | 20 |
| Purdue | Georgetown A | 10 | 0 | 0 | 10 |
| Northwestern B | Georgetown B | 10 | 0 | 0 | 10 |
| Notre Dame C | Iowa | 0 | 0 | 0 | 0 |
| Minnesota B | Carleton | 10 | 0 | 0 | 10 |
| Winona State | Wisconsin B | 10 | 0 | 0 | 10 |
| Alberta | UW B | 0 | 0 | 0 | 0 |
| UW A | UBC | 10 | 0 | 0 | 10 |
| Stanford B | Northwestern A | 10 | 10 | 10 | 30 |
| Notre Dame B | Notre Dame A | 0 | 0 | 0 | 0 |
| Texas A | TAMU | 10 | 10 | 0 | 20 |
| ASU | Texas B | 10 | 10 | 0 | 20 |
| 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 |
| Cambridge A | Warwick A | 10 | 10 | 0 | 20 |
| LSE | Cambridge B | 10 | 0 | 0 | 10 |
| Sheffield | Cambridge D | 10 | 10 | 0 | 20 |
| Cambridge E | Oxford B | 10 | 0 | 0 | 10 |
| Durham | Southampton B | 10 | 0 | 0 | 10 |
| Imperial A | Cambridge C | 10 | 10 | 0 | 20 |
| Imperial B | Southampton A | 10 | 0 | 0 | 10 |
| NYU C | Manchester | 10 | 0 | 0 | 10 |
| Oxford A | Oxford C | 10 | 10 | 0 | 20 |
| Bristol | Warwick B | 10 | 0 | 0 | 10 |
| Cornell B | Johns Hopkins A | 10 | 10 | 0 | 20 |
| Haverford A | George Washington A | 0 | 0 | 0 | 0 |
| John Jay College | Penn B | 10 | 10 | 0 | 20 |
| Maryland B | Haverford B | 10 | 0 | 0 | 10 |
| Maryland A | NYU A | 10 | 10 | 0 | 20 |
| Columbia C | NYU B | 10 | 10 | 0 | 20 |
| Columbia B | Penn A | 10 | 10 | 0 | 20 |
| Rutgers A | Vassar A | 10 | 10 | 0 | 20 |
| Binghamton A | Cornell D | 0 | 0 | 0 | 0 |
| Cornell C | RIT B | 10 | 0 | 0 | 10 |
| RIT A | ESF A | 10 | 10 | 0 | 20 |