Coriolis acceleration

Imagine two reference frames, one of which is fixed (\(S\)) and the other one is moving (\(S'\)). When the body is moving within a rotating coordinate system, its path deflects due to the appearance of the Coriolis acceleration on it. The object does not actually deviate from its path per se but it appears to do so because of the motion of the coordinate system.

Suppose a reference frame \(S'\) is fixed to a rotating body \(A\) (e.g. Earth), so that frame \(S'\) rotates w.r.t. another static reference frame \(S\). The Coriolis acceleration is the acceleration another body \(B\) has when moving within rotating reference frame \(S'\), so it is essentially zero for objects at rest in \(S'\).

Links:

  1. Wikipedia.

coriolis_acceleration_law(velocity_, angular_velocity_)[source]

Coriolis acceleration via relative velocity of body and angular velocity of rotation of \(S'\).

Law:

a_cor = 2 * cross(v_rel, w)

Latex:
\[{\vec a}_\text{cor} = 2 ({\vec v}_\text{rel} \times \vec \omega)\]
Parameters:

  • velocity_ –

    velocity of body relative to \(S'\)

    Symbol: v_rel

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

    Dimension: velocity

  • angular_velocity_ –

    angular velocity of rotation of \(S'\) relative to \(S\)

    Symbol: w

    Latex: \(\vec \omega\)

    Dimension: angle / time

Returns:

Coriolis acceleration of body in \(S'\)

Symbol: a_cor

Latex: \({\vec a}_\text{cor}\)

Dimension: acceleration