Rigid body

In physics, a rigid body is an idealisation of a solid body of finite dimension in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant regardless of external forces exerted on it.

The configuration space of a rigid body with one point fixed is given by the underlying manifold of the rotation group SO(3). This is just real projective space RP³. The configuration space of a nonfixed rigid body is

R³ × RP³,

the first factor accounting for translations.