Relative acceleration from force

Suppose reference frame \(S\) is fixed to a moving object (e.g. Earth). For some body \(B\) we can write an equation of motion in coordinates of \(S'\) akin to the Newton’s second law of motion for inertial frames, although we obtain two additional components to the equation: one corresponding to the Coriolis force, and another to the fictitious force of translation between inertial frame \(S\) and non-inertial frame \(S'\).

Links:

1. Wikipedia, derivable from here.

relative_acceleration

Vector of relative acceleration of body \(B\) relative to \(S'\)

Symbol:

a_rel

Latex:

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

Dimension:

acceleration

force

Vector of the net physical force exerted on body \(B\).

Symbol:

F

Latex:

\({\vec F}\)

Dimension:

force

mass

mass of body \(B\).

Symbol:

m

Latex:

\(m\)

Dimension:

mass

coriolis_acceleration

Vector of the Coriolis acceleration of body \(B\).

Symbol:

a_Cor

Latex:

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

Dimension:

acceleration

translation_acceleration

Vector of translation acceleration of body \(B\).

Symbol:

a_tr

Latex:

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

Dimension:

acceleration

law

a_rel = F / m + a_Cor - a_tr

Latex:

\[{\vec a}_\text{rel} = \frac{{\vec F}}{m} + {\vec a}_\text{Cor} - {\vec a}_\text{tr}\]