# Hamiltonian equations of motion Given a [[Momentum density]] $\pi(x)$ and a [[scalar field]] $\phi(x)$ the corresponding equations of motion are as follows.  and  # Relationship to the Lagrangian density Following from the typical [relationship between the Hamiltonian and the Lagrangian,](Hamiltonians.md#Relationship%20to%20the%20Lagrangian) We take the following [Legendre transformation](Legendre%20transformation.md) #Mechanics/ClassicalFields