Transport Theorem

The transport theorem, also called the transport equation, the rate-of-change transport theorem, the basic kinematic equation, or Bour's formula after Edmond Bour, is a vector equation relating a vector's time derivative as measured in a non-rotating coordinate system to its time derivative as measured in a rotating reference frame. Because a rotating frame's own axes change direction over time, even a vector that stays constant within that frame can appear to change when viewed from the non-rotating frame, and the transport theorem supplies the correction term, proportional to the frame's own angular velocity, that relates the two derivatives. It's used throughout classical mechanics, analytical dynamics and engineering to convert velocities and accelerations between rotating and fixed reference frames, and it's a distinct result from fluid mechanics' Reynolds transport theorem, despite the similar name.