We know that there is a physical interpretation for symplectic manifolds (briefly, the fact that a sympletic form assigns to any Hamiltoninan a vector field which describes the motion of particles). My question is if there is a physical meaning to the fact that all symplectic forms locally look alike, i.e. they are standard locally,(for instance, for the cotangent bundle of a manifold, what does it mean that any non-standard symplectic form locally looks like the standard one- which basically imposes the Hamilton's equations on the hamiltonian H)?