Classical Hamilton Equations

Available identifiers

WikidataQ1115699 ScholiaQ1115699MaRDI QIDQ6674257

classical equations of motion for systems described by a classical Hamilton function specifying the total energy

Description

Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities used in Lagrangian mechanics with (generalized) momenta. Both theories provide interpretations of classical mechanics and describe the same physical phenomena.

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Defining Formula: $\begin{array}{ccc}\frac{\mathrm{d}𝒒}{\mathrm{d}t}& =& +\frac{\partial \mathscr{H}}{\partial 𝒑}\\ \frac{\mathrm{d}𝒑}{\mathrm{d}t}& =& -\frac{\partial \mathscr{H}}{\partial 𝒒}\end{array}$

$H$ symbol represents Classical Hamilton Function

$p$ symbol represents Classical Momentum

$q$ symbol represents Classical Position

$t$ symbol represents Time

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Related URL

https://en.wikipedia.org/wiki/Hamiltonian_mechanics

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