Acceleration of transfer between relative frames

Imagine two reference frames, one of which is fixed (\(S\)) and the other one is moving (\(S'\)). The motion of a body stationary in moving frame \(S'\) due to the motion of the frame itself is called transfer motion. The acceleration related to such motion is called transfer acceleration. It is composed of the acceleration of the moving frame relative to the fixed frame, centripetal acceleration and the acceleration due to uneven rotation of the moving frame. The transfer acceleration only depends on the motion of frame \(S'\) relative to stationary frame \(S\), so its physical meaning would be that it is the acceleration in \(S\) of a point stationary in \(S'\).

Links:

  1. Wikipedia.

transfer_acceleration

Vector of the transfer acceleration.

Symbol:

a_tr

Latex:

\({\vec a}_\text{tr}\)

Dimension:

acceleration

moving_frame_acceleration

Vector of the acceleration of the \(S'\) relative to \(S\).

Symbol:

a_0

Latex:

\({\vec a}_{0}\)

Dimension:

acceleration

centripetal_acceleration

Vector of the body’s centripetal acceleration relative to \(S'\).

Symbol:

a_cp

Latex:

\({\vec a}_\text{cp}\)

Dimension:

acceleration

rotation_acceleration

Vector of acceleration due to non-uniform rotation of \(S'\).

Symbol:

a_rot

Latex:

\({\vec a}_\text{rot}\)

Dimension:

acceleration

law

a_tr = a_0 + a_cp + a_rot

Latex:
\[{\vec a}_\text{tr} = {\vec a}_{0} + {\vec a}_\text{cp} + {\vec a}_\text{rot}\]