For 10 points, name this operator that gives the total energy of a system.
A version of this operator used in the study of chaotic orbits around a galactic center has an extra term parametrized by a variable lambda and is named for Henon and Heiles. If the technique used to construct this operator is applied only to cyclic coordinates, then an operator named for Edward Routh is obtained. Constants of motion have a Poisson bracket of zero with this operator. Treating a system with n degrees of freedom in the framework of this operator gives rise to 2 n first-order (*) equations of motion. The time derivative of the distribution function equals its negative Poisson bracket with this operator according to Liouville's theorem. This operator, whose spatial derivative equals the negative time derivative of momentum according to one of its namesake's equations, can be constructed as the Legendre transform of the Lagrangian. For 10 points, name this operator that gives the total energy of a system.
A version of this operator used in the study of chaotic orbits around a galactic center has an extra term parametrized by a variable lambda and is named for Henon and Heiles.
Hamiltonian [or potential energy before "cyclic coordinates"]