Hamilton's equations of motion
Safko, John L. Formerly, Department of Physics and Astronomy, University of South Carolina, Columbia, South Carolina.
Stehle, Philip Department of Physics, University of Pittsburgh, Pittsburgh, Pennsylvania.
Last reviewed:August 2020
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A set of first-order ordinary differential equations that may be used to describe the motion of a mechanical system. Because of their remarkably symmetrical form [which appears in Eqs. (4), below], they are often referred to as the canonical equation of motion (where “canonical” is used in the sense of designating a simple general set of standard equations). The Lagrangian formulation of a system of f degrees of freedom generates f differential equations of second order in the time derivatives of the variables. Hamilton's equations, which are equivalent to Lagrange's equations, consist of 2f first-order and highly symmetrical equations. These properties make Hamilton's equations very useful for general discussions of the motion of systems. See also: Degree of freedom (mechanics); Differential equation; Lagrange's equations
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