A Coordinate free representation of Hamiltonian equations

Because a flow is defined in a coordinate-free form, the Hamilton equation can be defined in a coordinate-free manner as well. For further information, see, e.g., [3, 18, 20]. Differential 2-forms are generally represented by using a skew matrix in the same way. A differential form ω is closed if dω = 0 . Definition 3. A symplectic 2-form is a closed and non-degenerate differential 2-form.