Briefly on Mechanics of Cosserat���Zhilin

Our work is a step in the direction set by Newton and Euler to propose a general mathematical model for mechanical systems whose particles can experience displacements and turns with velocities v and ω. They are named as those of Cosserat–Zhilin and generate a new version of Newtonian mechanics based on notions of vector calculus – sliders and screw measures (bi–measures). In the case where Stocks theorem is applicable differential equations of motion or tensionare defined for main classes of Cosserat–Zhilin systems.The work defines multiplicative groups which represent the measure ofstress as a (well–defined) linear isotropic map of strain tensor or tensor ofstrain velocities for classical and polar continua in 2– and 3–dimensionalcases.