Abstract. We study geometrical constructions of a symplectic structure on the bundles of $k$-dimensional velocities of order $r$ by means of a symplectic structure on the base manifold. Then we determine all natural symplectic structures on the bundles $T^r_kT^*M$.
AMSclassification. 53C15, 58A20
Keywords. Symplectic structure, $k$-dimensional velocities