Absolute velocity of arbitrary motion

Imagine two reference frames, one of which is fixed (\(S\)) and the other one is moving arbitrarily (\(S'\)). The motion of the body relative to fixed frame \(S\) is called absolute motion. The motion of the body relative to moving frame \(S'\) is called relative motion. The motion of the body due to the motion of reference frame \(S'\) is called transfer motion. Absolute velocity is the sum of relative and transfer velocities.

Notes:

1. Moving frame \(S'\) can perform both translational and rotational motion.

Links:

1. Wikipedia.

absolute_velocity

Vector of velocity relative to fixed frame \(S\). See speed.

Symbol:

v_abs

Latex:

\({\vec v}_\text{abs}\)

Dimension:

velocity

relative_velocity

Vector of velocity relative to moving frame \(S'\). See speed.

Symbol:

v_rel

Latex:

\({\vec v}_\text{rel}\)

Dimension:

velocity

transfer_velocity

Vector of velocity due to movement of \(S'\) relative to \(S\). See speed.

Symbol:

v_tr

Latex:

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

Dimension:

velocity

law

v_abs = v_rel + v_tr

Latex:

\[{\vec v}_\text{abs} = {\vec v}_\text{rel} + {\vec v}_\text{tr}\]