Let $V$ be a submanifold of the cotangent bundle $T^*X$ of a smooth manifold $X$. Then we can consider the vector bundle $(TV)^{\bot}$ whose fiber is the symplectic orthogonal complement of a tangent space of $V$.
In some references, there is the statement: the vector bundle $(TV)^{\bot}$ is generated by Hamiltonian vector fields $X_f$ where $f$ vanishes on $V$.
I can check this in some particular cases. But I cannot prove this in general. If you know about that, please teach me.