| (1) | \frac{D {\bf u}}{Dt} = \frac{1}{\rho} \nabla {\bf \sigma} + {\bf g} |
where
( t, {\bf r} ) | time and spatial variables |
{\bf u}(t, {\bf r}) | velocity of Continuum Body |
\rho(t, {\bf r}) | density of Continuum Body |
\sigma(t, {\bf r}) | stress tensor of Continuum Body |
{\bf g}(t, {\bf r}) | sum of all body forces exerted on Continuum Body |
{\bf f}_{\rm cnt}(t, {\bf r}) | volumetric density of all contact forces exerted on Continuum Body |
\frac{D}{Dt} = \frac{\partial }{\partial t} + {\bf u} \nabla | Material derivative of the Continuum Body motion |
In Fluid Mechanics it's known as Navier–Stokes equation:
| (2) | \frac{D {\bf u}}{Dt} = \frac{\partial {\bf u}}{\partial t} + {\bf u} \nabla {\bf u} = \frac{1}{\rho} \nabla {\sigma} + {\bf g} |
See also
Physics / Mechanics / Continuum mechanics
[ Continuum Body ] [ Navier–Stokes equation ]