0 a function (= a mathematical relation) of an angle that is the reciprocal (= number) of tangent
1 a function (= mathematical relation) of an angle that is the reciprocal (= number) of tangent
Similarly, the second of equations (30) yields equation (32) and the inequality (33)with the tangent replaced by the minus cotangent.
The cotangent bundle of a manifold is equipped with a canonical symplectic form and a canonical section (the vertical section).
The metric g determines the isomorphism of the tangent and cotangent bundles.
This condition is particularly significant, being verified in all natural mechanical systems on cotangent bundles.
One of them is closely related to propagation of trajectories for symplectomorphisms of cotangent bundles.
This transformation has an invariant form that comes from the symplectic form in the cotangent bundle of the billiard table.
They may be geometrically interpreted as the forward propagation of tangents or the backward propagation of normals or cotangents.
But why should forces take values in the cotangent bundle?
