Grioli's Theorem with weights and the relaxed-polar mechanism of optimal Cosserat rotations

Andreas Fischle, Patrizio Neff

Let $F\in {\mathrm{GL}}^{+}(3)$ and consider the right polar decomposition $F=R_p(F)\cdot U$ into an orthogonal factor $R_p(F)\in \mathrm{SO}(3)$ and a symmetric, positive definite facto…