Acceleration due to non-uniform rotation

Imagine two reference frames, one of which is fixed (\(S\)) and the other is moving (\(S'\)). When \(S'\) rotates around \(S\) in a non-uniform way, the acceleration of some body \(B\) in \(S\) has a component corresponding to that non-uniform rotation of \(S'\). It is part of the transfer acceleration of body \(B\) in \(S\).

Notation:

1. \(\left[ \vec a, \vec b \right]\) (cross(a, b)) is vector product of \(\vec a\) and \(\vec b\).

Links:

1. Wikipedia.

non_uniform_rotation_acceleration

Vector of acceleration due to non-uniform rotation of \(S'\) relative to \(S\).

Symbol:

a_rot

Latex:

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

Dimension:

acceleration

time

time.

Symbol:

t

Latex:

\(t\)

Dimension:

time

angular_velocity

Pseudovector of the body’s angular velocity as a function of time. See angular_speed.

Symbol:

w(t)

Latex:

\({\vec \omega} \left( t \right)\)

Dimension:

angle/time

position_vector

The body’s position vector. See distance_to_origin.

Symbol:

r

Latex:

\({\vec r}\)

Dimension:

length

law

a_rot = cross(Derivative(w(t), t), r)

Latex:

\[{\vec a}_\text{rot} = \left[ \frac{d}{d t} {\vec \omega} \left( t \right), {\vec r} \right]\]