where θ θ L is the canonical momenta 1-form corresponding to the Lagrangian L . The vector field generating time translations is denoted by Δ Δ and the Lie derivative is denoted by L . One can use local charts ( q α α , q ˙ ˙ α α ) in which θ θ L = ∂ ∂ L ∂ ∂ q ˙ ˙ α α d q α α and Δ Δ := d d t = q ˙ ˙ α α ∂ ∂ ∂ ∂ q α α + q ¨ ¨ α α ∂ ∂ ∂ ∂ q ˙ ˙ α α and use coordinate expressions for the Lie derivative to see equivalence with coordinate expressions of the Euler Lagrange equation. The coordinate free form is particularly suitable for geometrical interpretation of the Euler Lagrange equations.