Editing Canonical coordinates (section)

==Generalized coordinates==
In [[Lagrangian mechanics]], a different set of coordinates are used, called the [[generalized coordinates]].  These are commonly denoted as <math>\left(q^i, \dot{q}^i\right)</math> with <math>q^i</math> called the '''generalized position''' and <math>\dot{q}^i</math> the '''generalized velocity'''.  When a [[symplectic vector field|Hamiltonian]] is defined  on the cotangent bundle, then the generalized coordinates are related to the canonical coordinates by means of the [[Hamilton–Jacobi equation]]s.