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]
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