Balance of linear momentum
= Balance of linear momentum
{title2=$\rho D\mathbf v/Dt=\nabla\cdot\boldsymbol\sigma+\rho\mathbf b$}
For a body occupying $V$, the rate of change of $\int_V\rho\mathbf v\,dV$ equals the <body forces> and surface <tractions>. With the <Cauchy stress tensor>, the local form is $\rho D\mathbf v/Dt=\nabla\cdot\boldsymbol\sigma+\rho\mathbf b$.