Every day we experiment motion and shape change of continuum media, assembly of different space dimension structures, fluids, solids which exhibit numerous evolutions either particular or general: large deformations, incompressibility, cavitation, contact, surface tension, defects, dislocations,... Stretch and rotation are a common feature of these motions and phenomenons. We base a continuum mechanics predictive theory on stretch and rotation quantified by matrices. The rigidifying system motions, investigated in this Chapter, depend on the interactions of the frame with the structure. In case of no interactions they are the classical rigid body motions. In case of interactions, for instance contact of the frame with the structure, the power of the internal forces accounts for these interactions. Some examples are given.