Notice that in contrast to the [[Hamiltonians]] the _Lagrangian_ is _velocity dependent_. A basic definition of the Lagrangian is given here in terms of [Generalized coordinates](Generalized%20coordinates.md). # Relationship to the Hamiltonian The Lagrangian of a system may be derived from its [[Hamiltonians]] via a [Legendre transformation](Legendre%20transformation.md) given as follows. # In terms of Lagrangian Density #Mechanics