Dynamic torque

The dynamic Torseur is a mathematical tool used during the application of the Basic principle of dynamics.

Definition

The dynamic torque as all the torques is the reduction of a vector field in a point in two particular vectors.

Its notation is the following one: ${\ mathcal {D} (S/R)} _ {Has} =
\begin{Bmatrix}
\ overrightarrow {\ mathcal {has}} (S/R) \ \
\ overrightarrow {\ delta _A} (S/R)
\end{Bmatrix}_{A/R}$

with R locates study, S solid studied, does not have unspecified a solid S.

Quantity of acceleration

The vector $\ overrightarrow {\ mathcal {has}} (S/R)$ represents the quantity of acceleration of the solid. The quantity of acceleration is expressed in $kg.m.s^ {- 2}$

There is $\ overrightarrow {\ mathcal {has}} (S/R) = m \ vec \ Gamma (G/R) = \ int_ {(S)} {\ vec \ Gamma (P \ in S/R) DM}$ .

With G center of gravity of S.

Dynamic moment

The vector $\ overrightarrow {\ delta _A} (S/R)$ is the dynamic moment.

There is $\ overrightarrow {\ delta _A} (S/R) = \ int_ {(S)} {\ vec {AP} \ wedge \ vec \ Gamma (P \ in S/R) DM}$ .

Particular cases

In the case of a solid only in translation, one has ${\ mathcal {D} (S/R)} _ {G} =$

\begin{Bmatrix} m \ overrightarrow {has _ {G/R}} \ \ \ overrightarrow {0} \end{Bmatrix}_{G/R}

In the case of a solid only in rotation around its axis of symmetry and its center of gravity on the axis of rotation noted $\ vec Z$ , one has ${\ mathcal {D} (S/R)} _ {G} =$

\begin{Bmatrix} \ overrightarrow {0} \ \ I \ ddot \ theta \ vec Z \end{Bmatrix}_{G/R}

with I Moment of inertia of S expressed in $kg.m^2$ and $\ ddot \ theta$ angular acceleration in $rad.s ^ {- 2}$ .

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