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 --
Readers familiar with more advanced mathematics such as cotangent bundles, exterior derivatives and symplectic manifolds should read the related symplectomorphism article.
Abstractly, it is a second order operator on each exterior power of the cotangent bundle.
Important examples of vector bundles include the tangent bundle and cotangent bundle of a smooth manifold.
Likewise, cotangent space is a contravariant functor, essentially the composition of the tangent space with the dual space above.
For mechanical systems, the phase space usually consists of all possible values of position and momentum variables (i.e. the cotangent space of configuration space).
Typically, the cotangent space is defined as the dual space of the tangent space at "x", although there are more direct definitions (see below).
This is more or less what is done when a tangent linear code is first developed and then the partials are used in the cotangent linear, or adjoint code.
But why should forces take values in the cotangent bundle?
