An Etymological Dictionary of Astronomy and Astrophysics

One of a set of equations that describe the motion of a → dynamical system in terms of the → Hamiltonian function and the → generalized coordinates. For a → holonomic system with n degrees of freedom, Hamilton’s equations are expressed by: q^._i = ∂H/∂p_i and p^._i = - ∂H/∂q_i, i = 1, …, n.

See also: → Hamiltonian function; → equation.