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

Vector of the body’s Coriolis acceleration in \(S'\).

Symbol:

a_Cor

Latex:

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

Dimension:

acceleration

relative_velocity

Vector of the body’s velocity relative to \(S'\). See speed.

Symbol:

v_rel

Latex:

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

Dimension:

velocity

angular_velocity

Pseudovector of the angular velocity of the body’s rotation. See angular_speed.

Symbol:

w

Latex:

\({\vec \omega}\)

Dimension:

angle/time

law

a_Cor = 2 * cross(v_rel, w)

Latex:

\[{\vec a}_\text{Cor} = 2 \left[ {\vec v}_\text{rel}, {\vec \omega} \right]\]