Cardinal equations of mechanics

The cardinal equations of mechanics are a system of two equations that fully determine the dynamics of a system. They are

\left\{\begin{align} \mathbf{F}^{(e)}=\frac{d\mathbf{p}}{dt} \\ \mathbf{N}^{(e)}_{\Omega}=\frac{d\mathbf{L}_\Omega}{dt} \end{align}\right.

where $\mathbf{F}^{(e)}$ is the total external force and $\mathbf{N}^{(e)}_{\Omega}$ is the total external moment of force about the axis $\Omega$ . $\mathbf{p}$ is the linear momentum of the center of mass and $\mathbf{L}_{\Omega}$ is its angular momentum.

If both equations are equal to zero, the object is in equilibrium.