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_law(relative_velocity_, transfer_velocity_)[source]

Absolute velocity via relative and transfer velocities.

Law:

v_abs = v_rel + v_tr

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

  • relative_velocity_ –

    velocity relative to moving frame \(S'\)

    Symbol: v_rel

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

    Dimension: velocity

  • transfer_velocity_ –

    velocity due to movement of frame \(S'\) relative to frame \(S\)

    Symbol: v_tr

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

    Dimension: velocity

Returns:

velocity relative to fixed frame \(S\)

Symbol: v_abs

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

Dimension: velocity

relative_velocity_law(absolute_velocity_, transfer_velocity_)[source]

Relative velocity via absolute and transfer velocities.

Law:

v_rel = v_abs - v_tr

Latex:
\[{\vec v}_\text{rel} = {\vec v}_\text{abs} - {\vec v}_\text{tr}\]
Parameters:

  • absolute_velocity_ –

    velocity relative to fixed frame \(S\)

    Symbol: v_abs

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

    Dimension: velocity

  • transfer_velocity_ –

    velocity due to movement of frame \(S'\) relative to frame \(S\)

    Symbol: v_tr

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

    Dimension: velocity

Returns:

velocity relative to moving frame \(S'\)

Symbol: v_rel

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

Dimension: velocity

transfer_velocity_law(absolute_velocity_, relative_velocity_)[source]

Transfer velocity via absolute and relative velocities.

Law:

v_tr = v_abs - v_rel

Latex:
\[{\vec v}_\text{tr} = {\vec v}_\text{abs} - {\vec v}_\text{rel}\]
Parameters:

  • absolute_velocity_ –

    velocity relative to fixed frame \(S\)

    Symbol: v_abs

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

    Dimension: velocity

  • relative_velocity_ –

    velocity relative to moving frame \(S'\)

    Symbol: v_rel

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

    Dimension: velocity

Returns:

velocity due to movement of frame \(S'\) relative to frame \(S\)

Symbol: v_tr

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

Dimension: velocity