Velocity relative to reference frame

For any reference frame, whether it is inertial or not, the motion relative to it can be described using the position vector relative to that frame’s origin.

Links:

  1. Wikipedia.

  2. Wikipedia (ru).

relative_velocity_law(position_, time_)[source]

Velocity relative to \(S\).

Law:

v_rel = Derivative(r(t), t)

Latex:
\[{\vec v}_\text{rel} = \frac{d \vec r}{d t}\]
Parameters:

  • position_ –

    radius vector, or position vector, of body in \(S\) as a function of time

    Symbol: r(t)

    Latex: \(\vec r(t)\)

    Dimension: length

  • time_ –

    time

    Symbol: t

    Dimension: time

Returns:

velocity relative to \(S\)

Symbol: v_rel

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

Dimension: velocity

relative_position_law(initial_position_, velocity_, time_)[source]

Final position via initial position and velocity as a function of time.

Law:

r = r_0 + Integral(v_rel(t), t)

Latex:
\[\vec r = {\vec r}_0 + \int {\vec v}_\text{rel}(t) dt\]
Parameters:

  • initial_position_ –

    position vector in \(S\) at \(t = 0\)

    Symbol: r_0

    Latex: \({\vec r}_0\)

    Dimension: length

  • velocity_ –

    velocity relative to \(S\) as a function of time

    Symbol: v_rel(t)

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

    Dimension: velocity

  • time_ –

    time

    Symbol: t

    Dimension: time

Returns:

position vector in \(S\) at time \(t\)

Symbol: r

Latex: \(\vec r\)

Dimension: length