Hamiltonian mechanics

In <a href="/facts/Physics/a7aH2y08">physics</a>, Hamiltonian mechanics is a reformulation of <a href="/facts/Lagrangian_mechanics/sTxyqWz8">Lagrangian mechanics</a> that emerged in 1833. Introduced by <a href="/facts/Sir_William_Rowan_Hamilton/U86CqUlt">Sir William Rowan Hamilton</a>, Hamiltonian mechanics replaces (generalized) velocities 
 
 
 
 
 
 
 
 q
 ˙
 
 
 
 
 i
 
 
 
 
 {\displaystyle {\dot {q}}^{i}}
 
 used in Lagrangian mechanics with (generalized) momenta. Both theories provide interpretations of <a href="/facts/Classical_mechanics/ykG8upsN">classical mechanics</a> and describe the same physical phenomena.
Hamiltonian mechanics has a close relationship with geometry (notably, <a href="/facts/Symplectic_geometry/runXFCea">symplectic geometry</a> and <a href="/facts/Poisson_structure/LvAmEzul">Poisson structures</a>) and serves as a <a href="/facts/Hamilton%25E2%2580%2593Jacobi_equation/XM0R7nzD">link</a> between classical and <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>.

Hamiltonian mechanics open-in-new

Hamiltonian mechanics