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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 the real projective space
RP3. The configuration space of a nonfixed rigid body is just R3 ×
RP3, the first factor accounting for translations.
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