= Symmetry and positivity of a rigid-body resistance matrix
{title2=$\binom{\mathbf F}{\mathbf G}=\mathsf R\binom{\mathbf U}{\boldsymbol\Omega},\quad\mathsf R^T=\mathsf R,\quad q^T\mathsf Rq>0$}
Here $\mathbf F,\mathbf G$ are forces and torques exerted by the body on the fluid, or the external force and torque needed to maintain its motion. The <Lorentz reciprocal theorem for Stokes flow> makes the six-dimensional <hydrodynamic resistance matrix> symmetric. The power identity $\mathbf F\cdot\mathbf U+\mathbf G\cdot\boldsymbol\Omega=2\mu\int e:e\,dV$ makes it a <positive-definite matrix> for a body moving in otherwise stationary unbounded fluid.
Back to article page
