Varignon

$\mathcal{M}(\mathrm{B}) = \mathcal{M}(\mathrm{A}) + \overrightarrow{\mathrm{BA}} \wedge \overrightarrow{\mathcal{R}}$

Statique/Actions Mécaniques

$\{\mathcal{T}_{2/1} \} = \begin{matrix} \\ \\ \end{matrix}_\mathrm{A} \begin{Bmatrix} \vec{\mathcal{R}}_{2/1} \\ \vec{\mathcal{M}}_{{A,2/1}} \end{Bmatrix}_\mathfrak{R}$

Cinématique

$\{\mathcal{V}_{\mathrm{S/R}}\}= \vec{\mathrm{V}}_{S/R} = \begin{matrix} \\ \\ \end{matrix}_\mathrm{A} \begin{Bmatrix} \vec{\Omega}_{S/R} \\ \vec{\mathrm{V}}_{A,S/R} \end{Bmatrix}_\mathfrak{R}$

Cinétique

$\{\mathcal{C}_{\mathrm{S/R}}\} = \vec{\sigma} _\mathrm{S/R} = \begin{matrix} \\ \\ \end{matrix}_\mathrm{A} \begin{Bmatrix} m \cdot \vec{\mathrm{V}}_\mathrm{G,S/R} \\ \vec{\sigma} _\mathrm{A,S/R} \end{Bmatrix}_\mathfrak{R}$

$\vec{\sigma}_\mathrm{S/R}(A) = \mathrm{I_{A,S}} \cdot \vec \Omega_\mathrm{S/R} + \overrightarrow{\mathrm{AG}} \wedge m\vec{\mathrm{V}}_\mathrm{A,S/R}$

Dynamique

$\{{ \mathcal{D}_{\mathrm{S/R}}}\} = \begin{matrix} \\ \\ \end{matrix}_\mathrm{A} \begin{Bmatrix} {m \cdot \vec{\mathcal{\Gamma}}}_\mathrm{G,S/R} \\ \vec{\delta}_\mathrm{A,S/R} \end{Bmatrix}_\mathfrak{R}$

$\vec{\delta}_\mathrm{A,S/R} = \frac{\mathrm{d}}{\mathrm{d}t} \vec{\sigma}_\mathrm{A,S/R} + m \cdot \vec{\mathrm{V}}_\mathrm{A,S/R} \wedge \vec{\mathrm{V}}_\mathrm{G,S/R}$

TEC

$T_{S/R} = \frac{1}{2} \{ \mathcal{C}_{\mathrm{S/R}} \} \otimes \{ \mathcal{V}_{\mathrm{S/R}} \}$

$P_{\Sigma\rightarrow S,S/R} = \{ \mathcal{T}_{\Sigma\rightarrow S} \} \otimes \{ \mathcal{V}_{S/R} \}$

$P_{1\rightarrow 2,2/1} = \{ \mathcal{T}_{1\rightarrow 2} \} \otimes \{ \mathcal{V}_{2/1} \}$

$\frac{dT_{S/R}}{dt} = \mathcal{P}_{ext/R} + \mathcal{P_{int}}$