How come a rigid body has 6 degrees of freedoms (DOFs) ? Isn't velocity a DOF?

Question

For rigid body we need to know position of three points and their velocities to determine everything. So that would make 12 DOF. Why do text books say it has six DOFs?

Answer 1

A rigid body has 6 configuration degrees of freedom because its most general configuration can be obtained by translating (3 degrees of freedom) and rotating (3 degrees of freedom) its initial configuration. A mathy way of saying this is that its configuration manifold is $\mathbb R^3\times \mathrm{SO}(3)$.

However, you are right that the phase space of a rigid body is 12-dimensional because each independent configuration degree of freedom corresponds to an independent momentum degree of freedom.