Theoretical foundations of overvector structures in general problems of machine introduction

Abstract

Currently, there is a helical calculus, as a vector algebra of complex vectors of motion of solids in space. The article shows that the helical calculus is not a complete description of the motion of solids. Since, the helical calculus describes only the movement along a helical line, and does not take into account the movement with flips. The article shows that for a complete description of the motion of solids in space, it is necessary to introduce a new algebra of motion with a revolution ("calculus of wheels"), similar to the algebra of screws. The introduction of an additional algebra of complex vectors of turns (wheels) entails the need to develop an algebra of bicomplex (Hypercomplex) vectors of "motors" describing a complete combination of all types of movements of solids in space. Keywords: helical calculus, solid, vector, space, motion with revolution, helical line, wheel motion, bicomplex vector