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 . 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...