This results in the force equation (equivalent to the Euler–Lagrange equation) p ˙ ˙ = − − ∂ ∂ H ∂ ∂ x = q x ˙ ˙ ⋅ ⋅ ( ∇ ∇ A ) − − q ∇ ∇ φ φ = q ∇ ∇ ( x ˙ ˙ ⋅ ⋅ A ) − − q ∇ ∇ φ φ from which one can derive d d t ( m x ˙ ˙ 1 − − x ˙ ˙ 2 c 2 ) = d d t ( p − − q A ) = p ˙ ˙ − − q ∂ ∂ A ∂ ∂ t − − q ( x ˙ ˙ ⋅ ⋅ ∇ ∇ ) A = q ∇ ∇ ( x ˙ ˙ ⋅ ⋅ A ) − − q ∇ ∇ φ φ − − q ∂ ∂ A ∂ ∂ t − − q ( x ˙ ˙ ⋅ ⋅ ∇ ∇ ) A = q E + q x ˙ ˙ × × B