#cotangent bundle

[isomorphismes]

In many mechanics problems, the phase space is the cotangent bundle of a configuration space.

José Natário

Glossary

tangent bundle means stuff attached to a point (eg, a wind attached to a point above Chicago)

co- has a couple (sometimes related) meanings, in this case "Go from X over A to Maps from X to A."

phase spaces and configuration spaces are two cases where a mathematisation of the physical world is definitely not going to be merely 3-D. We might attach a zillion particles to a 3-D grid, but the model would be zillion-dimensional, not 3-dimensional.

[ernestyalumni]

Given any Riemannian manifold M (smooth mnfd, equip w/ metric g, simply a 2-tensor), tangent & cotangent bundle on M are isomorphic via g!