An Etymological Dictionary of Astronomy and Astrophysics
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The study of → dynamical systems in terms of the → Hamilton's equations.

→ Hamiltonian function; → dynamics.

A reformulation of classical mechanics that predicts the same outcomes as classical mechanics. → Hamiltonian dynamics.

→ Hamiltonian; → mechanics.

A function that describes the motion of a → dynamical system in terms of the → Lagrangian function, → generalized coordinates, → generalized momenta, and time. For a → holonomic system having n degrees of freedom, the Hamiltonian function is of the form: H = Σp_iq^._i - L(q_i,q^._i,t) (summed from i = 1 to n), where L is the Lagrangian function. If L does not depend explicitly on time, the system is said to be → conservative and H is the total energy of the system. The Hamiltonian function plays a major role in the study of mechanical systems. Also called → Hamiltonian.

Introduced in 1835 by the Irish mathematician and physicist William Rowan Hamilton (1805-1865); → function.

The dynamical operator in → quantum mechanics that corresponds to the → Hamiltonian function in classical mechanics.

→ Hamiltonian function; → operator.