Hamiltonian Mechanics

Reformulation of mechanics in coordinates and momenta via Hamilton's equations, bridging classical dynamics and quantum theory.

Specifications & Metrics

symbol

q̇ = ∂H/∂p, ṗ = −∂H/∂q

Core Principles & Analysis

• Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833, introduced by Sir William Rowan Hamilton.
• Hamilton's founding 1833 paper gave 'a general method of expressing the paths of light, and of the planets'.
• Hamilton's equations are 2n first-order differential equations, while Lagrange's equations are n second-order equations.

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Sources

• Wikipedia: Hamiltonian mechanics