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Hamiltonian Mechanics ○𓆪｜Definition｜1st｜20251119205401-00-⌔

Hamiltonian mechanics - Wikipedia

Hamiltonian mechanics

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In physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by Sir William Rowan Hamilton,¹ Hamiltonian mechanics replaces (generalized) velocities ${\dot{q}}^i$ used in Lagrangian mechanics with (generalized) momenta. Both theories provide interpretations of classical mechanics and describe the same physical phenomena.

Hamiltonian mechanics has a close relationship with geometry (notably, symplectic geometry and Poisson structures) and serves as a link between classical and quantum mechanics.

Printed 2026-06-28.

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Footnotes

1. Hamilton, William Rowan, Sir (1833). On a general method of expressing the paths of light, & of the planets, by the coefficients of a characteristic function. Printed by P.D. Hardy. OCLC 68159539. ↩

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