Hamiltonian

Reexpression of Newtonian mechanics that takes positions and momenta and gives you energy. A Hamiltonian system is usefully well-behaved in a variety of ways - eigenvalues all have mirrors, the system is integrable, independence from positions gives you invariance in moments (this last seems useful as hell when thinking about curried expressions / logic but I haven't figured out how yet. Likely to be pursuable from Structure and Interpretation of Classical Mechanics). Source: Hamiltonian Systems - Scholarpedia