# AMC-TXT source
# Interrogation écrite de mécanique - dynamique

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Lang: FR
Code: 3
ShuffleQuestions: 0
LaTeX-Preambule:\usepackage{graphicx}
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DefaultScoringS: e=0,v=0,b=1,m=-0.5
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Title: [* Interrogation écrite de cinématique *]

Presentation: [* L'ensemble du questionnaire est basé sur la description distribuée en annexe *]

[[\smallbreak]]
 
[[\smallbreak]]
Remplir au [*stylo NOIR*] et si vous effacez, mettre du blanc correcteur, [* y compris sur le cadre *] pour éviter les faux positifs. 

Ecrire votre nom, et, pour vous identifier automatiquement, coder le n°étudiant qui vous a été donné préalablement.
[[\smallbreak]]
En l'absence d'indications, une seule réponse est correcte. La bonne réponse donne un point, une mauvaise -0,5, rien 0
[[\smallbreak]]

Certaines questions font apparaître le symbole [[\multiSymbole{}]] et peuvent présenter zéro, une ou plusieurs bonnes réponses. 

La note pour une question est obtenue en ajoutant 1 point par case coché juste et en enlevant 0,5 points par case cochée fausse. 

Cocher "aucune de ces réponses n'est correcte" [*et*] une autre case vaut 0
[[\smallbreak]]

# SeparateAnswerSheet: 1
# AnswerSheetTitle: interrogation ecrite de mécanique - cinématique

[* QUESTIONS *]

*([shuffle=true,columns=1,group=matpass,numquestions=2] [* Matrices de passage *] 

*[id=P01,columns=3] Que vaut la matrice de passage [[$P_{01}$]] ?
+ [[$ \left(\begin{array}{ccc}\cos(\theta) & -\sin(\theta) & 0 \\ \sin(\theta) & \cos\theta) & 0 \\ 0 & 0 & 1 \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\theta) & \sin(\theta) & 0 \\ -\sin(\theta) & \cos\theta) & 0 \\ 0 & 0 & 1 \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\theta) & 0 & \sin(\theta) \\ 0 & 1 & 0 \\ -\sin(\theta) & 0 & \cos\theta) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\theta) & 0 & -\sin(\theta) \\ 0 & 1 & 0 \\ \sin(\theta) & 0 & \cos\theta) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc} 1 & 0 & 0 \\ 0 & cos(\theta) & \sin(\theta) \\ 0 & -\sin(\theta) & \cos\theta) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\sin(\theta) & -\cos(\theta) & 0 \\ \cos(\theta) & \sin\theta) & 0 \\ 0 & 0 & 1 \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\theta) & -\sin(\theta) & 0 \\ -\sin(\theta) & \cos\theta) & 0 \\ 0 & 0 & 1 \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\theta) & -\sin(\theta) & 0 \\ 0 & \cos(\theta) & \sin\theta) \\ 0 & 0 & 1 \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\theta) & -\sin(\theta) & 0 \\ -\sin(\theta) & \cos\theta) & 0 \\ 0 & 0 & \cos\theta) \end{array}\right)$]]

*[id=P10,columns=3] Que vaut la matrice de passage [[$P_{10}$]] ?
+ [[$ \left(\begin{array}{ccc}\cos(\theta) & \sin(\theta) & 0 \\ -\sin(\theta) & \cos\theta) & 0 \\ 0 & 0 & 1 \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\theta) & -\sin(\theta) & 0 \\ \sin(\theta) & \cos\theta) & 0 \\ 0 & 0 & 1 \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\theta) & 0 & \sin(\theta) \\ 0 & 1 & 0 \\ -\sin(\theta) & 0 & \cos\theta) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\theta) & 0 & -\sin(\theta) \\ 0 & 1 & 0 \\ \sin(\theta) & 0 & \cos\theta) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc} 1 & 0 & 0 \\ 0 & cos(\theta) & \sin(\theta) \\ 0 & -\sin(\theta) & \cos\theta) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\sin(\theta) & -\cos(\theta) & 0 \\ \cos(\theta) & \sin\theta) & 0 \\ 0 & 0 & 1 \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\theta) & -\sin(\theta) & 0 \\ -\sin(\theta) & \cos\theta) & 0 \\ 0 & 0 & 1 \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\theta) & -\sin(\theta) & 0 \\ 0 & \cos(\theta) & \sin\theta) \\ 0 & 0 & 1 \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\theta) & -\sin(\theta) & 0 \\ -\sin(\theta) & \cos\theta) & 0 \\ 0 & 0 & \cos\theta) \end{array}\right)$]]


*[id=P12,columns=3] Que vaut la matrice de passage [[$P_{12}$]] ?
+ [[$ \left(\begin{array}{ccc}\cos(\alpha) & 0 & \sin(\alpha) \\ 0 & 1 & 0 \\ -\sin(\alpha) & 0 & \cos\alpha) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\alpha) & 0 & -\sin(\alpha) \\ 0 & 1 & 0 \\ \sin(\alpha) & 0 & \cos\alpha) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\alpha) & -\sin(\alpha) & 0 \\ \sin(\alpha) & \cos\alpha) & 0 \\ 0 & 0 & 1 \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\alpha) & \sin(\alpha) & 0 \\ -\sin(\alpha) & \cos\alpha) & 0 \\ 0 & 0 & 1 \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc} 1 & 0 & 0 \\ 0 & cos(\alpha) & \sin(\alpha) \\ 0 & -\sin(\alpha) & \cos\alpha) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\sin(\alpha) & 0 & -\cos(\alpha) \\ 0 & 1 & 0 \\ \cos(\alpha) & 0 & \sin\alpha) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\alpha) & 0 & \sin(\alpha)  \\ 0 & 1 & 0 \\ sin(\alpha) & 0 & \cos\alpha)  \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\alpha) & \sin(\alpha) & 0 \\ 0 & 1 & 0 \\ 0 & \sin\alpha) & \cos(\alpha) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\alpha) & 0 & \sin(\alpha)  \\ 0 & \cos\alpha) & 0 \\ -\sin(\alpha) & 0 & \cos\alpha) \end{array}\right)$]]

*[id=P21,columns=3] Que vaut la matrice de passage [[$P_{21}$]] ?
+ [[$ \left(\begin{array}{ccc}\cos(\alpha) & 0 & -\sin(\alpha) \\ 0 & 1 & 0 \\ \sin(\alpha) & 0 & \cos\alpha) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\alpha) & 0 & \sin(\alpha) \\ 0 & 1 & 0 \\ -\sin(\alpha) & 0 & \cos\alpha) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\alpha) & -\sin(\alpha) & 0 \\ \sin(\alpha) & \cos\alpha) & 0 \\ 0 & 0 & 1 \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\alpha) & \sin(\alpha) & 0 \\ -\sin(\alpha) & \cos\alpha) & 0 \\ 0 & 0 & 1 \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc} 1 & 0 & 0 \\ 0 & cos(\alpha) & \sin(\alpha) \\ 0 & -\sin(\alpha) & \cos\alpha) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\sin(\alpha) & 0 & -\cos(\alpha) \\ 0 & 1 & 0 \\ \cos(\alpha) & 0 & \sin\alpha) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\alpha) & 0 & \sin(\alpha)  \\ 0 & 1 & 0 \\ sin(\alpha) & 0 & \cos\alpha)  \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\alpha) & \sin(\alpha) & 0 \\ 0 & 1 & 0 \\ 0 & \sin\alpha) & \cos(\alpha) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\alpha) & 0 & \sin(\alpha)  \\ 0 & \cos\alpha) & 0 \\ -\sin(\alpha) & 0 & \cos\alpha) \end{array}\right)$]]

*[id=P13,columns=3] Que vaut la matrice de passage [[$P_{13}$]] ?
+ [[$ \left(\begin{array}{ccc} 1 & 0 & 0 \\ 0 & cos(\varphi) & -\sin(\varphi) \\ 0 & \sin(\varphi) & \cos\varphi) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc} 1 & 0 & 0 \\ 0 & cos(\varphi) & \sin(\varphi) \\ 0 & -\sin(\varphi) & \cos\varphi) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\varphi) & -\sin(\varphi) & 0 \\ \sin(\varphi) & \cos\varphi) & 0 \\ 0 & 0 & 1 \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\varphi) & \sin(\varphi) & 0 \\ -\sin(\varphi) & \cos\varphi) & 0 \\ 0 & 0 & 1 \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\varphi) & 0 & -\sin(\varphi) \\ 0 & 1 & 0 \\ \sin(\varphi) & 0 & \cos\varphi) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\varphi) & \sin(\varphi) & 0 \\ 0 & 1 & 0 \\ -\sin(\varphi) & 0 & \cos\varphi) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc} 1 & 0 & 0 \\ 0 & \cos(\varphi) & -\sin(\varphi) \\0 & -\sin(\varphi) & \cos\varphi) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc} 1 & 0 & 0 \\ 0 & \sin(\varphi) & -\cos(\varphi) \\ 0 & \cos(\varphi) & \sin\varphi) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\varphi) & 0 & 0 \\0 & \cos(\varphi) & -\sin(\varphi) \\ 0 & \sin(\varphi) & \cos\varphi) \end{array}\right)$]]

*[id=P31,columns=3] Que vaut la matrice de passage [[$P_{31}$]] ?
+ [[$ \left(\begin{array}{ccc} 1 & 0 & 0 \\ 0 & cos(\varphi) & \sin(\varphi) \\ 0 & -\sin(\varphi) & \cos\varphi) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc} 1 & 0 & 0 \\ 0 & cos(\varphi) & -\sin(\varphi) \\ 0 & \sin(\varphi) & \cos\varphi) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\varphi) & -\sin(\varphi) & 0 \\ \sin(\varphi) & \cos\varphi) & 0 \\ 0 & 0 & 1 \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\varphi) & \sin(\varphi) & 0 \\ -\sin(\varphi) & \cos\varphi) & 0 \\ 0 & 0 & 1 \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\varphi) & 0 & -\sin(\varphi) \\ 0 & 1 & 0 \\ \sin(\varphi) & 0 & \cos\varphi) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\varphi) & \sin(\varphi) & 0 \\ 0 & 1 & 0 \\ -\sin(\varphi) & 0 & \cos\varphi) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc} 1 & 0 & 0 \\ 0 & \cos(\varphi) & -\sin(\varphi) \\0 & -\sin(\varphi) & \cos\varphi) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc} 1 & 0 & 0 \\ 0 & \sin(\varphi) & -\cos(\varphi) \\ 0 & \cos(\varphi) & \sin\varphi) \end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos(\varphi) & 0 & 0 \\0 & \cos(\varphi) & -\sin(\varphi) \\ 0 & \sin(\varphi) & \cos\varphi) \end{array}\right)$]]

*)

*([shuffle=true,columns=1,group=prodmatpass,numquestions=1] [* Matrices de passage *] 

*[id=P02,columns=2,next] Que vaut la matrice de passage P02 ?
+ [[$\left(\begin{array}{ccc}\cos \left(\mathrm{α}\right) \cos \left(\mathrm{θ}\right)&-\sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{α}\right)\\\cos \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right)&\sin \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)\\-\sin \left(\mathrm{α}\right)&0&\cos \left(\mathrm{α}\right)\end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos \left(\mathrm{α}\right) \cos \left(\mathrm{θ}\right)&-\cos \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)&\sin \left(\mathrm{α}\right)\\\sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right)&0\\-\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{α}\right)&\sin \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{α}\right)\end{array}\right)$]]
- [[$\left(\begin{array}{ccc}\cos \left(\mathrm{α}\right) \cos \left(\mathrm{θ}\right)&\cos \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)&-\sin \left(\mathrm{α}\right)\\-\sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right)&0\\\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{α}\right)&\sin \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{α}\right)\end{array}\right)$]]
- [[$\left(\begin{array}{ccc}\cos \left(\mathrm{α}\right) \cos \left(\mathrm{θ}\right)&\sin \left(\mathrm{θ}\right)&-\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{α}\right)\\-\cos \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right)&\sin \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)\\\sin \left(\mathrm{α}\right)&0&\cos \left(\mathrm{α}\right)\end{array}\right)$]]
- [[$\left(\begin{array}{ccc}\cos \left(\mathrm{θ}\right)&\cos \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)&0\\-\sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right)\cos \left(\mathrm{α}\right)&-\sin \left(\mathrm{α}\right)\\\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{α}\right)&\sin \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{α}\right)\end{array}\right)$]]
- [[$\left(\begin{array}{ccc}\cos \left(\mathrm{α}\right)&\sin \left(\mathrm{θ}\right)&-\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{α}\right)\\-\cos \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right)&\sin \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)\\0&\sin \left(\mathrm{α}\right)&\cos \left(\mathrm{α}\right) \cos \left(\mathrm{θ}\right)\end{array}\right)$]]

*[id=P20,columns=2,next] Que vaut la matrice de passage P20 ?
+ [[$\left(\begin{array}{ccc}\cos \left(\mathrm{α}\right) \cos \left(\mathrm{θ}\right)&\cos \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)&-\sin \left(\mathrm{α}\right)\\-\sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right)&0\\\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{α}\right)&\sin \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{α}\right)\end{array}\right)$]]
- [[$\left(\begin{array}{ccc}\cos \left(\mathrm{α}\right) \cos \left(\mathrm{θ}\right)&-\sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{α}\right)\\\cos \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right)&\sin \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)\\-\sin \left(\mathrm{α}\right)&0&\cos \left(\mathrm{α}\right)\end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos \left(\mathrm{α}\right) \cos \left(\mathrm{θ}\right)&-\cos \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)&\sin \left(\mathrm{α}\right)\\\sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right)&0\\-\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{α}\right)&\sin \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{α}\right)\end{array}\right)$]]
- [[$\left(\begin{array}{ccc}\cos \left(\mathrm{α}\right) \cos \left(\mathrm{θ}\right)&\sin \left(\mathrm{θ}\right)&-\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{α}\right)\\-\cos \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right)&\sin \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)\\\sin \left(\mathrm{α}\right)&0&\cos \left(\mathrm{α}\right)\end{array}\right)$]]
- [[$\left(\begin{array}{ccc}\cos \left(\mathrm{θ}\right)&\cos \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)&0\\-\sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right)\cos \left(\mathrm{α}\right)&-\sin \left(\mathrm{α}\right)\\\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{α}\right)&\sin \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{α}\right)\end{array}\right)$]]
- [[$\left(\begin{array}{ccc}\cos \left(\mathrm{α}\right)&\sin \left(\mathrm{θ}\right)&-\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{α}\right)\\-\cos \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right)&\sin \left(\mathrm{α}\right) \sin \left(\mathrm{θ}\right)\\0&\sin \left(\mathrm{α}\right)&\cos \left(\mathrm{α}\right) \cos \left(\mathrm{θ}\right)\end{array}\right)$]]


*[id=P03,columns=2] Que vaut la matrice de passage P03 ?
+ [[$\left(\begin{array}{ccc}\cos \left(\mathrm{θ}\right)&-\cos \left(\mathrm{φ}\right) \sin \left(\mathrm{θ}\right)&\sin \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)\\\sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right) \cos \left(\mathrm{φ}\right)&-\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)\\0&\sin \left(\mathrm{φ}\right)&\cos \left(\mathrm{φ}\right)\end{array}\right)$]]
- [[$\left(\begin{array}{ccc}\cos \left(\mathrm{θ}\right)&\sin \left(\mathrm{θ}\right)&0\\-\cos \left(\mathrm{φ}\right) \sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right) \cos \left(\mathrm{φ}\right)&\sin \left(\mathrm{φ}\right)\\\sin \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)&-\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)&\cos \left(\mathrm{φ}\right)\end{array}\right)$]]
- [[$\left(\begin{array}{ccc}\cos \left(\mathrm{θ}\right)&\cos \left(\mathrm{φ}\right) \sin \left(\mathrm{θ}\right)&\sin \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)\\-\sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right) \cos \left(\mathrm{φ}\right)&\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)\\0&-\sin \left(\mathrm{φ}\right)&\cos \left(\mathrm{φ}\right)\end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos \left(\mathrm{θ}\right)&-\sin \left(\mathrm{θ}\right)&0\\\cos \left(\mathrm{φ}\right) \sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right) \cos \left(\mathrm{φ}\right)&-\sin \left(\mathrm{φ}\right)\\\sin \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)&\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)&\cos \left(\mathrm{φ}\right)\end{array}\right)$]]
- [[$\left(\begin{array}{ccc}\cos \left(\mathrm{θ}\right)&\cos \left(\mathrm{φ}\right) \sin \left(\mathrm{θ}\right)&\sin \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)\\-\sin \left(\mathrm{θ}\right)& \cos \left(\mathrm{φ}\right)&\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)\\-\sin \left(\mathrm{φ}\right)& 0 &\cos \left(\mathrm{θ}\right) \cos \left(\mathrm{φ}\right)\end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos \left(\mathrm{θ}\right)\cos \left(\mathrm{φ}\right) & 0 & -\sin \left(\mathrm{θ}\right)\\\cos \left(\mathrm{φ}\right) \sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right) &-\sin \left(\mathrm{φ}\right)\\\sin \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)&\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)&\cos \left(\mathrm{φ}\right)\end{array}\right)$]]

*[id=P30,columns=2] Que vaut la matrice de passage P30 ?
+ [[$\left(\begin{array}{ccc}\cos \left(\mathrm{θ}\right)&\sin \left(\mathrm{θ}\right)&0\\-\cos \left(\mathrm{φ}\right) \sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right) \cos \left(\mathrm{φ}\right)&\sin \left(\mathrm{φ}\right)\\\sin \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)&-\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)&\cos \left(\mathrm{φ}\right)\end{array}\right)$]]
- [[$\left(\begin{array}{ccc}\cos \left(\mathrm{θ}\right)&-\cos \left(\mathrm{φ}\right) \sin \left(\mathrm{θ}\right)&\sin \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)\\\sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right) \cos \left(\mathrm{φ}\right)&-\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)\\0&\sin \left(\mathrm{φ}\right)&\cos \left(\mathrm{φ}\right)\end{array}\right)$]]
- [[$\left(\begin{array}{ccc}\cos \left(\mathrm{θ}\right)&\cos \left(\mathrm{φ}\right) \sin \left(\mathrm{θ}\right)&\sin \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)\\-\sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right) \cos \left(\mathrm{φ}\right)&\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)\\0&-\sin \left(\mathrm{φ}\right)&\cos \left(\mathrm{φ}\right)\end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos \left(\mathrm{θ}\right)&-\sin \left(\mathrm{θ}\right)&0\\\cos \left(\mathrm{φ}\right) \sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right) \cos \left(\mathrm{φ}\right)&-\sin \left(\mathrm{φ}\right)\\\sin \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)&\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)&\cos \left(\mathrm{φ}\right)\end{array}\right)$]]
- [[$\left(\begin{array}{ccc}\cos \left(\mathrm{θ}\right)&\cos \left(\mathrm{φ}\right) \sin \left(\mathrm{θ}\right)&\sin \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)\\-\sin \left(\mathrm{θ}\right)& \cos \left(\mathrm{φ}\right)&\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)\\-\sin \left(\mathrm{φ}\right)& 0 &\cos \left(\mathrm{θ}\right) \cos \left(\mathrm{φ}\right)\end{array}\right)$]]
- [[$ \left(\begin{array}{ccc}\cos \left(\mathrm{θ}\right)\cos \left(\mathrm{φ}\right) & 0 & -\sin \left(\mathrm{θ}\right)\\\cos \left(\mathrm{φ}\right) \sin \left(\mathrm{θ}\right)&\cos \left(\mathrm{θ}\right) &-\sin \left(\mathrm{φ}\right)\\\sin \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)&\cos \left(\mathrm{θ}\right) \sin \left(\mathrm{φ}\right)&\cos \left(\mathrm{φ}\right)\end{array}\right)$]]
*)

*([shuffle=true,group=TauxRotation,numquestions=3] [*questions de cinématique*]

*[id=OmegaR2R1,horiz] [[$\overrightarrow{\omega(R_{2}/R_{1})}$]] = 
+ [[$\dot{\alpha}\, \vec{y_{1}}$]]
- [[$-\dot{\alpha}\, \vec{y_{1}}$]]
-{-1} [[$\alpha\, \vec{y_{1}}$]]
- [[$-\dot{\alpha}\, \vec{x_{1}}$]]
- [[$\dot{\alpha}\, \vec{x_{2}}$]]
- [[$\dot{\alpha}\, \vec{z_{1}}$]]
- [[$-\dot{\alpha}\, \vec{z_{2}}$]]

*[id=OmegaR1R0,horiz] [[$\overrightarrow{\omega(R_{1}/R_{0})}$]] = 
+ [[$\dot{\theta}\, \vec{z_{1}}$]]
- [[$-\dot{\theta}\, \vec{z_{1}}$]]
-{-1} [[$\theta\, \vec{z_{0}}$]]
- [[$-\dot{\theta}\, \vec{x_{1}}$]]
- [[$\dot{\theta}\, \vec{x_{0}}$]]
- [[$\dot{\theta}\, \vec{y_{1}}$]]
- [[$\-\dot{\theta}\, \vec{y_{0}}$]]

*[id=OmegaR2R0,columns=4] [[$\overrightarrow{\omega(R_{2}/R_{0})}$]] = 
- [[$\dot{\alpha}\, \vec{x_{1}}$]]
+ [[$\dot{\alpha}\, \vec{y_{1}} + \dot{\theta}\, \vec{z_{1}}$]]
- [[$-\dot{\alpha}\, \vec{y_{1}} + \dot{\theta}\, \vec{z_{0}}$]]
- [[$\dot{\alpha}\, \vec{x_{1}} + \dot{\theta}\, \vec{z_{1}}$]]
- [[$-\dot{\alpha}\, \vec{z_{2}} + \dot{\theta}\, \vec{x_{1}}$]]
- [[$-\dot{\alpha}\, \vec{y_{0}} + \dot{\theta}\, \vec{z_{0}}$]]
- [[$\dot{\alpha}\, \vec{y_{1}} - \dot{\theta}\, \vec{z_{1}}$]]
- [[$-\dot{\alpha}\, \vec{y_{1}} - \dot{\theta}\, \vec{z_{1}}$]]

*[id=OmegaR3R1,horiz] [[$\overrightarrow{\omega(R_{3}/R_{1})}$]] = 
+ [[$\dot{\varphi}\, \vec{x_{1}}$]]
- [[$-\dot{\varphi}\, \vec{x_{1}}$]]
-{-1} [[$\varphi\, \vec{x_{1}}$]]
- [[$-\dot{\varphi}\, \vec{y_{1}}$]]
- [[$\dot{\varphi}\, \vec{y_{3}}$]]
- [[$\dot{\varphi}\, \vec{z_{1}}$]]
- [[$-\dot{\varphi}\, \vec{z_{3}}$]]

*[id=OmegaR3R0,columns=4] [[$\overrightarrow{\omega(R_{3}/R_{0})}$]] = 
- [[$\dot{\varphi}\, \vec{x_{1}}$]]
+ [[$\dot{\varphi}\, \vec{x_{1}} + \dot{\theta}\, \vec{z_{1}}$]]
- [[$-\dot{\varphi}\, \vec{x_{1}} + \dot{\theta}\, \vec{z_{0}}$]]
- [[$\dot{\varphi}\, \vec{y_{1}} + \dot{\theta}\, \vec{z_{1}}$]]
- [[$-\dot{\varphi}\, \vec{z_{3}} + \dot{\theta}\, \vec{x_{1}}$]]
- [[$-\dot{\varphi}\, \vec{x_{0}} + \dot{\theta}\, \vec{z_{0}}$]]
- [[$\dot{\varphi}\, \vec{x_{1}} - \dot{\theta}\, \vec{z_{1}}$]]
- [[$-\dot{\varphi}\, \vec{x_{1}} - \dot{\theta}\, \vec{z_{1}}$]]
*)


*([shuffle=true,columns=1,numquestions=1,group=VitessesRotationAxeFixe]

*[id=VAR0,columns=5] Que vaut [[$\overrightarrow{V(A/R_{0})}$]]
+ [[$r \,\dot{\theta}\, \vec{y_{1}}$]]
- [[$r \,\dot{\theta} \,\vec{x_{1}}$]]
- [[$r \,\dot{\theta} \,\vec{z_{1}}$]]
- [[$-r \,\dot{\theta} \,\vec{x_{1}}$]]
- [[$-r \,\dot{\theta} \,\vec{y_{2}}$]]
- [[$r \,\dot{\theta} \cos(\theta)\,\vec{y_{0}}$]]
- [[$r \,\dot{\theta} \sin(\theta)\,\vec{x_{0}}$]]
-{-1} [[$r \,\theta \,\vec{y_{1}}$]]
-{-1} [[$\dot{r} \, \dot{\theta} \vec{y_{1}}$]]
- [[$\dot{r} \, \vec{x_{2}}+r \, \dot{\theta} \,\vec{y_{2}}$]]

*[id=VCR0,columns=5] Que vaut [[$\overrightarrow{V(C/R_{0})}$]]
+ [[$-r \,\dot{\theta}\, \vec{x_{1}}$]]
- [[$r \,\dot{\theta} \,\vec{x_{1}}$]]
- [[$r \,\dot{\theta} \,\vec{z_{1}}$]]
- [[$-r \,\dot{\theta} \,\vec{y_{1}}$]]
- [[$-r \,\dot{\theta} \,\vec{z_{2}}$]]
- [[$-r \,\dot{\theta} \cos(\theta)\,\vec{x_{0}}$]]
- [[$r \,\dot{\theta} \sin(\theta)\,\vec{y_{0}}$]]
-{-1} [[$-r \,\theta \,\vec{x_{1}}$]]
-{-1} [[$-\dot{r} \, \dot{\theta} \vec{x_{1}}$]]
- [[$\dot{r} \, \vec{y_{1}}+r \, \dot{\theta} \,\vec{x_{1}}$]]

*[id=VBR1,columns=5] Que vaut [[$\overrightarrow{V(B/R_{1})}$]]
+ [[$-L \,\dot{\alpha}\, \vec{z_{2}}$]]
- [[$L \,\dot{\alpha} \,\vec{z_{2}}$]]
- [[$L \,\dot{\alpha} \,\vec{x_{2}}$]]
- [[$L \,\dot{\alpha} \,\vec{y_{2}}$]]
- [[$-L \,\dot{\alpha} \,\vec{y_{2}}$]]
-{-1} [[$-L \,\alpha \,\vec{z_{2}}$]]
-{-1} [[$L \,\alpha \,\vec{z_{2}}$]]
-{-1} [[$\dot{L}\, \dot{\alpha} \vec{x_{2}}$]]
- [[$\dot{L} \, \vec{y_{2}}+L\, \dot{\alpha} \,\vec{z_{2}}$]]
- [[$-\dot{L} \, \vec{y_{2}}-L\, \dot{\alpha} \,\vec{z_{2}}$]]

*[id=VDR1,columns=5] Que vaut [[$\overrightarrow{V(D/R_{1})}$]]
+ [[$L \,\dot{\varphi}\, \vec{y_{3}}$]]
- [[$-L \,\dot{\varphi} \,\vec{y_{3}}$]]
- [[$L \,\dot{\varphi} \,\vec{x_{3}}$]]
- [[$L \,\dot{\varphi} \,\vec{z_{3}}$]]
- [[$-L \,\dot{\varphi} \,\vec{z_{3}}$]]
-{-1} [[$-L \,\varphi \,\vec{y_{3}}$]]
-{-1} [[$L \,\varphi \,\vec{y_{3}}$]]
-{-1} [[$\dot{L}\, \dot{\varphi} \vec{y_{3}}$]]
- [[$\dot{L} \, \vec{z_{3}}-L\, \dot{\varphi} \,\vec{y_{3}}$]]
- [[$-\dot{L} \, \vec{z_{3}}-L\, \dot{\varphi} \,\vec{y_{3}}$]]

*)

*([shuffle=true,columns=1,numquestions=1,group=vitessesR0]

*[id=VBR0,columns=3] Que vaut [[$\overrightarrow{V(B /R_{0})}$]]
+ [[$(r+L \cos(\alpha)) \,\dot{\theta}\, \vec{y_{1}}-L\,\dot\alpha\,\vec{z_{2}}$]]
- [[$r\,\dot{\theta}\, \vec{y_{1}}-L\,\dot\alpha\,\vec{z_{2}}$]]
- [[$(r+L \sin(\alpha)) \,\dot{\theta}\, \vec{y_{1}}-L\,\dot\alpha\,\vec{z_{2}}$]]
- [[$(r+L) \,\dot{\theta}\, \vec{y_{1}}-L\,\dot\alpha\,\vec{z_{2}}$]]
- [[$r\,\dot{\theta}\, \vec{y_{1}}+L\,\dot{\theta}\, \vec{y_{2}} -L\,\dot\alpha\,\vec{z_{2}}$]]
- [[$(r+L \cos(\alpha)) \,\dot{\theta}\, \vec{y_{1}}+L\,\dot\alpha\,\vec{z_{2}}$]]
- [[$-(r+L \sin(\alpha)) \,\dot{\theta}\, \vec{y_{1}}-L\,\dot\alpha\,\vec{z_{2}}$]]
- [[$-(r+L \cos(\alpha)) \,\dot{\theta}\, \vec{y_{1}}+L\,\dot\alpha\,\vec{z_{2}}$]]

*[id=VDR0,columns=3] Que vaut [[$\overrightarrow{V(D /R_{0})}$]]
+ [[$-(r+L \sin(\varphi)) \,\dot{\theta}\, \vec{x_{1}}+L\,\dot\varphi\,\vec{y_{3}}$]]
- [[$-r \,\dot{\theta}\, \vec{x_{1}}+L\,\dot\varphi\,\vec{y_{3}}$]]
- [[$-(r+L \cos(\varphi)) \,\dot{\theta}\, \vec{x_{1}}+L\,\dot\varphi\,\vec{y_{3}}$]]
- [[$-(r+L) \,\dot{\theta}\, \vec{x_{1}}+L\,\dot\varphi\,\vec{y_{3}}$]]
- [[$-r \,\dot{\theta}\, \vec{x_{1}}-L \,\dot{\theta}\, \vec{x_{2}} +L\,\dot\varphi\,\vec{y_{3}}$]]
- [[$-(r+L \sin(\varphi)) \,\dot{\theta}\, \vec{x_{1}}-L\,\dot\varphi\,\vec{y_{3}}$]]
- [[$ (r+L \sin(\varphi)) \,\dot{\theta}\, \vec{x_{1}}+L\,\dot\varphi\,\vec{y_{3}}$]]
- [[$(r+L \sin(\varphi)) \,\dot{\theta}\, \vec{x_{1}}-L\,\dot\varphi\,\vec{y_{3}}$]]

*)

*([shuffle=true,columns=1,numquestions=1,groupe=TorseurCinematique] [* Torseur cinématique *]

**[id=V2R0,columns=2] [[$\left\{ V(2/0)\right\} =$]] ... cocher les réponses exactes
+ [[$\begin{array}{c} \\ \\ \\ \end{array}_{A}\left\{ \begin{array}{cc} 0 & 0\\ \dot{\alpha} & r\,\dot\theta\\ \dot \theta & 0 \end{array}\right\} _{R_{1}}$]]
+ [[$\begin{array}{c} \\ \\ \\ \end{array}_{B}\left\{ \begin{array}{cc} 0 & -L \,\sin(\alpha)\,\dot{\alpha}\\ \dot{\alpha} & (r+L\,\cos(\alpha))\,\dot\theta\\ \dot\theta & -L\,\cos(\alpha)\,\dot\alpha \end{array}\right\} _{R_{1}}$]]
+ [[$\begin{array}{c} \\ \\ \\ \end{array}_{A}\left\{ \begin{array}{cc} -\dot\theta\,\sin(\alpha) & 0\\ \dot{\alpha} & r\,\dot\theta\\ \dot \theta\,\cos(\alpha) & 0 \end{array}\right\} _{R_{2}}$]]
+ [[$\begin{array}{c} \\ \\ \\ \end{array}_{B}\left\{ \begin{array}{cc} -\dot\theta\,\sin(\alpha) & 0\\ \dot{\alpha} & (r+L\,\cos(\alpha))\,\dot\theta\\ \dot \theta\,\cos(\alpha) & -L \,\dot\alpha \end{array}\right\} _{R_{2}}$]]
- [[$\begin{array}{c} \\ \\ \\ \end{array}_{A}\left\{ \begin{array}{cc} 0 & 0 \\ r\,\dot\theta & \dot{\alpha} \\ 0 & \dot \theta \end{array}\right\} _{R_{1}}$]]
- [[$\begin{array}{c} \\ \\ \\ \end{array}_{B}\left\{ \begin{array}{cc} 0 & 0 \\ \dot{\alpha} & (r+L\,\cos(\alpha))\,\dot\theta\\ \dot\theta & -L \,\dot\alpha \end{array}\right\} _{R_{1}}$]]
- [[$\begin{array}{c} \\ \\ \\ \end{array}_{B}\left\{ \begin{array}{cc} 0 & 0\\ \dot{\alpha} & (r+L\,\cos(\alpha))\,\dot\theta\\ \dot \theta & -L \,\dot\alpha \end{array}\right\} _{R_{2}}$]]

**[id=V3R0,columns=2] [[$\left\{ V(3/0)\right\} =$]] ... cocher les réponses exactes
+ [[$\begin{array}{c} \\ \\ \\ \end{array}_{C}\left\{ \begin{array}{cc} \dot\varphi & - r \,\dot\theta \\ 0 & 0 \\ \dot \theta & 0 \end{array}\right\} _{R_{1}}$]]
+ [[$\begin{array}{c} \\ \\ \\ \end{array}_{D}\left\{ \begin{array}{cc} \dot\varphi & -(r+L \,\sin(\varphi))\,\dot{\theta}\\ 0 & L\,\cos(\varphi)\,\dot\varphi\\ \dot\theta & L \,\sin(\varphi)\,\dot\varphi \end{array}\right\} _{R_{1}}$]]
+ [[$\begin{array}{c} \\ \\ \\ \end{array}_{C}\left\{ \begin{array}{cc} \dot\varphi & - r \,\dot{\theta} \\ \sin(\varphi) \dot{\theta} & 0\\ \cos(\varphi) \dot \theta & 0 \end{array}\right\} _{R_{3}}$]]
+ [[$\begin{array}{c} \\ \\ \\ \end{array}_{D}\left\{ \begin{array}{cc} \dot\varphi & -(r+L \,\sin(\varphi))\,\dot{\theta} \\ \sin(\varphi) \dot{\theta} & L\,\dot\varphi \\ \cos(\varphi) \dot \theta & 0 \end{array}\right\} _{R_{3}}$]]
- [[$\begin{array}{c} \\ \\ \\ \end{array}_{C}\left\{ \begin{array}{cc} - r \,\dot\theta & \dot\varphi \\ 0 & 0 \\ 0 & \dot \theta \end{array}\right\} _{R_{1}}$]]
- [[$\begin{array}{c} \\ \\ \\ \end{array}_{D}\left\{ \begin{array}{cc} \dot\varphi & -(r+L \,\sin(\varphi))\,\dot{\theta}\\ 0 & L\,\dot\varphi\\ \dot\theta & 0 \end{array}\right\} _{R_{1}}$]]
- [[$\begin{array}{c} \\ \\ \\ \end{array}_{C}\left\{ \begin{array}{cc} \dot\varphi & - r \,\dot{\theta} \\ 0 & 0\\ \dot \theta & 0 \end{array}\right\} _{R_{3}}$]]
*)

*([shuffle=true,columns=1,group=accelerationsrotation,numquestions=1] [* Accélérations *]

*[id=aBover1,columns=3] que vaut [[$\overrightarrow{\gamma(B/R_{1})}$]]
+ [[$-L\,\ddot{\alpha} \,\vec{z_{2}}-L {\dot{\alpha}}^2 \, \vec{x_{2}}$]]
- [[$ L\,\ddot{\alpha} \,\vec{z_{2}}$]]
- [[$ L{\dot{\alpha}}^2 \, \vec{x_{2}}$]]
- [[$ L\,\ddot{\alpha} \,\vec{z_{2}}+L{\dot{\alpha}}^2 \, \vec{x_{2}}$]]
- [[$ r \,\ddot{\theta} \,\vec{y_{1}}-r{\dot{\theta}}^2 \, \vec{x_{1}}-L\,\ddot{\alpha} \,\vec{z_{2}}-L {\dot{\alpha}}^2 \, \vec{x_{2}}$]]
- [[$ r \,\ddot{\theta} \,\vec{y_{1}}-r{\dot{\theta}}^2 \, \vec{x_{1}}+L\,\ddot{\alpha} \,\vec{z_{2}}$]]

*[id=aAover0,columns=3] que vaut [[$\overrightarrow{\gamma(A/R_{0})}$]]
+ [[$ r \,\ddot{\theta} \,\vec{y_{1}}-r\,{\dot{\theta}}^2 \, \vec{x_{1}}$]]
- [[$ r \,\ddot{\theta} \,\vec{y_{1}}$]]
- [[$ -r \, {\dot{\theta}}^2 \, \vec{x_{1}}$]]
- [[$ -r \,\ddot{\theta} \,\vec{y_{1}}-r {\dot{\theta}}^2 \, \vec{x_{1}}$]]
- [[$ r \,\ddot{\theta} \,\vec{y_{1}}+r\, {\dot{\theta}}^2 \, \vec{x_{1}}$]]
-{-1} [[$ \dot r \,\ddot{\theta} \,\vec{y_{1}}-\dot r\,{\dot{\theta}}^2 \, \vec{x_{1}}$]]


*[id=aDover1,columns=3] Que vaut [[$\overrightarrow{\gamma(D/R_{1})}$]]
+ [[$ L\,\ddot{\varphi} \,\vec{y_{3}}+L {\dot{\varphi}}^2 \,\vec{z_{3}}$]]
- [[$ L\,\ddot{\varphi} \,\vec{y_{3}}$]]
- [[$ L{\dot{\varphi}}^2 \, \vec{z_{3}}$]]
- [[$ -L\,\ddot{\varphi} \,\vec{y_{3}}-L{\dot{\varphi}}^2 \, \vec{z_{3}}$]]
- [[$ -r \,\ddot{\theta} \,\vec{x_{1}}-r{\dot{\theta}}^2 \, \vec{y_{1}}+L\,\ddot{\varphi} \,\vec{y_{3}}+L {\dot{\varphi}}^2 \, \vec{x_{3}}$]]
- [[$ -r \,\ddot{\theta} \,\vec{x_{1}}-r{\dot{\theta}}^2 \, \vec{y_{1}}+L\,\ddot{\varphi} \,\vec{y_{3}}$]]

*[id=aCover0,columns=3] que vaut [[$\overrightarrow{\gamma(C/R_{0})}$]]
+ [[$ -r \,\ddot{\theta} \,\vec{x_{1}}-r\,{\dot{\theta}}^2 \, \vec{y_{1}}$]]
- [[$ -r \,\ddot{\theta} \,\vec{x_{1}}$]]
- [[$ -r \, {\dot{\theta}}^2 \, \vec{y_{1}}$]]
- [[$ r \,\ddot{\theta} \,\vec{x_{1}}-r {\dot{\theta}}^2 \, \vec{y_{1}}$]]
- [[$ r \,\ddot{\theta} \,\vec{x_{1}}+r\, {\dot{\theta}}^2 \, \vec{y_{1}}$]]
-{-1} [[$ \dot r \,\ddot{\theta} \,\vec{x_{1}}-\dot r \,{\dot{\theta}}^2 \, \vec{y_{1}}$]]

*)

*([shuffle=true,columns=1,group=accelerations,numquestions=1] [* Accélérations *]

*[id=aBover0] que vaut [[$\overrightarrow{\gamma(B/R_{0})}$]]
+ [[$ -(r+L\,\cos(\alpha))\,{\dot{\theta}}^2 \vec{x_1} +((r+L\,\cos(\alpha))\,\ddot{\theta}-2\,L\,\sin(\alpha)\,\dot\alpha\,\dot\theta)\,\vec{y_{1}}-L {\dot{\alpha}}^2\,\vec{x_{2}}-L \ddot{\alpha}\,\vec{z_{2}}$]]
- [[$ -r \,{\dot{\theta}}^2 \vec{x_1} +r\,\ddot{\theta}\,\vec{y_{1}}-L {\dot{\alpha}}^2\,\vec{x_{1}}-L \ddot{\alpha}\,\vec{z_{2}}$]]
- [[$ -(r+L)\,{\dot{\theta}}^2 \vec{x_1} +(r+L)\,\ddot{\theta}\,\vec{y_{1}}+L {\dot{\alpha}}^2\,\vec{x_{2}}+L \ddot{\alpha}\,\vec{z_{2}}$]]
- [[$ (r+L\,\cos(\alpha))\,{\dot{\theta}}^2 \vec{x_1} -(r+L\,\cos(\alpha))\,\ddot{\theta}\,\vec{y_{1}}-L {\dot{\alpha}}^2\,\vec{x_{2}}-L \ddot{\alpha}\,\vec{z_{2}}$]]
- [[$ L\,\cos(\alpha)\,{\dot{\theta}}^2 \vec{x_1} +(L\,\cos(\alpha)\,\ddot{\theta}-2\,L\,\sin(\alpha)\,\dot\alpha\,\dot\theta)\,\vec{y_{1}}-L {\dot{\alpha}}^2\,\vec{x_{2}}-L \ddot{\alpha}\,\vec{z_{2}}$]]
- [[$ (r+L\,\cos(\alpha))\,{\dot{\theta}}^2 \vec{x_1} -((r+L\,\cos(\alpha))\,\ddot{\theta}+2\,L\,\sin(\alpha)\,\dot\alpha\,\dot\theta)\,\vec{y_{1}}+L {\dot{\alpha}}^2\,\vec{x_{2}}+L \ddot{\alpha}\,\vec{z_{2}}$]]

*[id=aDover0] que vaut [[$\overrightarrow{\gamma(D/R_{0})}$]]
+ [[$ -((r+L\,\sin(\varphi))\,\ddot{\theta}+2\,L\,\cos(\varphi)\,\dot\varphi\,\dot\theta)\,\vec{x_{1}}-(r+L\,\sin(\varphi))\,{\dot{\theta}}^2 \vec{y_1}+L \ddot{\varphi}\,\vec{y_{3}}+L {\dot{\varphi}}^2\,\vec{z_{3}}$]]
- [[$ -r\,\ddot{\theta}\,\vec{x_{1}}-r \,{\dot{\theta}}^2 \vec{y_1} +L \ddot{\varphi}\,\vec{y_{3}}+L {\dot{\varphi}}^2\,\vec{z_{3}}$]]
- [[$ -(r+L)\,\ddot{\theta}\,\vec{x_{1}}-(r+L)\,{\dot{\theta}}^2 \vec{y_1}+L \ddot{\varphi}\,\vec{y_{3}}+L {\dot{\varphi}}^2\,\vec{z_{3}}$]]
- [[$ -(r+L\,\sin(\varphi))\,\ddot{\theta}\,\vec{x_{1}}-(r+L)\,\sin(\varphi)\,{\dot{\theta}}^2 \vec{y_1}+L \ddot{\varphi}\,\vec{y_{3}}+L {\dot{\varphi}}^2\,\vec{z_{3}}$]]
- [[$ (L\,\sin(\varphi)\ddot{\theta}+2\,L\,\cos(\varphi)\,\dot\varphi\,\dot\theta)\,\vec{x_{1}}-L\,\sin(\varphi)\,{\dot{\theta}}^2 \vec{y_1}+L \ddot{\varphi}\,\vec{y_{3}}+L {\dot{\varphi}}^2\,\vec{z_{3}}$]]
- [[$ ((r+L\,\sin(\varphi))\,\ddot{\theta}-2\,L\, \cos(\varphi)\,\dot\varphi\,\dot\theta)\,\vec{x_{1}}+(r+L\,\sin(\varphi))\,{\dot{\theta}}^2 \vec{y_1}+L \ddot{\varphi}\,\vec{y_{3}}+L {\dot{\varphi}}^2\,\vec{z_{3}}$]]
*)




