nLab position space

In physical applications, a differential manifold $M$ is often used to parametrize the possible positions of particles in a system. In such models, $M$ is often called the “position space”.

Manifolds and bundles which are derived from $M$ also receive convenient names. The tangent bundle $TM$ is called the “configuration space”, since the configuration of the system is specifying positions and velocity vectors. The cotangent bundle $T^* M$ is called the “phase space” (why?).

A partial list follows.

Manifold	Manifold Name
$M$	Position Space
$TM$	Configuration Space
$T^* M$	Phase Space

Reference: Betancourt and Stein. The Geometry of Hamiltonian Monte Carlo