Fr.: dynamique hamiltonienne
The study of → dynamical systems in terms of the → Hamilton's equations.
→ Hamiltonian function; → dynamics.
Fr.: formalisme de Hamilton
A reformulation of classical mechanics that predicts the same outcomes as classical mechanics. → Hamiltonian dynamics.
→ Hamiltonian; → mechanics.
Fr.: fonction de Hamilton
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 = Σpiq.i - L(qi,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.
Fr.: opérateur hamiltonien
The dynamical operator in → quantum mechanics that corresponds to the → Hamiltonian function in classical mechanics.
→ Hamiltonian function; → operator.