Position and speed of a point on the rigid body

• The center of mass has, at time \(t\),
• • - a position \(p(t)\)
  • - a velocity \(p'(t)=v(t)\)

• The body has an orientation \(\mathrm{R}(t)\)

• A point of the rigid body has

• • - a position
    \(p_i(t)=p(t)+R(t)\,r_0\)

• • - a speed
    \(p'_i(t)=v(t)+R'(t)\,r_0\)