Polar Decomposition Theorem

This lecture covers the Polar Decomposition Theorem, which explains how a deformation can be decomposed into a stretch followed by a rotation or vice versa. It also delves into the uniqueness of the stretch and rotation components, as well as the procedure to generate them from the deformation gradient. The lecture explores the concept of positive definite matrices and the symmetrical nature of the stretch tensor. Additionally, it discusses the calculation of the rotation tensor from the stretch tensor and the implications of the theorem in continuum mechanics.