I know that in fluid dynamics,we use Lagrangian formulation of acceleration. That is, $\frac{dv}{dt}=\frac{\delta v}{\delta t}+(v.\nabla )v$ . My question is can we use the same formulation for rigid body kinematics because it seems quite general and if we can  ,why don't we see it being used anywhere in classical mechanics.

I know that in fluid dynamics, we use Lagrangian description of acceleration. That is, a material derivative $$\frac{dv}{dt}=\frac{\partial v}{\partial t}+(v\cdot\nabla )v .$$ My question is can we use the same formulation for rigid body kinematics because it seems quite general and if we can, why don't we see it being used anywhere in classical mechanics?