1. The problem statement, all variables and given/known data In rigid body, r is the position of a rigid body relative to world coordinates, dr/dt is the rate of change of r in world coordinates. I encountered the term Dr/Dt as the rate of change of r in world coordinates relative to the body coordinates system. And that Dr/Dt = dr/dt-wxr My question is, how does Dr/Dt is called? (terminology) Also the operator D/Dt has the same rules as the operator d/dt, how do you proove it? There is some relationship to proove this, but what is this relation ship? 2. Relevant equations Dr/Dt = dr/dt-wxr 3. The attempt at a solution I tried to use Dr/Dt = dr/dt-wxr to proove that both operators has the same rules, but didnt succed. In matter of fact, I found some contradiction. For instance: d(AxB)/dt = Ax(dB/dt)+(dA/dt)xB So D(AxB)/Dt = Ax(DB/Dt)+(DA/Dt)xB should also be true. However using Dr/Dt = dr/dt-wxr showed that there is inequality. Thank you.