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I'm looking for details regarding the derivation of a formula called in French" loi de composition des accélérations" ( " composition of accelerations law").

This law allows you ( as far as I understand it) to determine the absolute acceleration ( relative to a fixed referential R) of a point $M$ moving in an accelerated referential $R'$ using the following formula :

$\vec a= \vec a'+\vec a_e+\vec a_c$

with

  • vector $\vec a$ = absolute acceleration of $M$ in $R$

  • vector $\vec a_e$ = acceleration of a fixed point coinciding with $M$ at $t$ in $R'$ ( " acceleration d'entraînement" in french)

  • and $\vec a_c$ = the ( so called) Coriolis acceleration.

I'm been searching google for " composition of accelerations" and " addition of accelerations" without much results.

So, I'd like to know the English equivalent in order to get more informations on the web regarding this formula.

Also, I'd be interested in knowing in which chapters of English/American physics textbooks ( and of what level textbooks) I'm likely to find a derivation of this formula. In French textbooks it is treated commonly in chapters called " change of referential" ( " changement de référentiel").

Thanks in advance.

Source : this document in French , page 17 / 42

http://olivier.granier.free.fr/PC-Montesquieu445072/cariboost_files/Changement-ref-1516.pdf

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    $\begingroup$ Maybe this? Your question would be much clearer if you gave the formulas for $a_e$ and $a_c$, and if you specified how $S’$ is moving relative to $S$. $\endgroup$
    – G. Smith
    Commented Mar 31, 2021 at 21:06
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    $\begingroup$ The law of addition of accelerations, or just “addition of accelerations”, or “addition of accelerations in different (non-inertial) frames”. $\endgroup$
    – ZeroTheHero
    Commented Mar 31, 2021 at 22:02

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