Nonclassical Periodic Functions: Their Calculation and Applications

Abstract

A system of continuous T-periodic functions, which express the values of Cartesian coordinates of a moving point as functions of the traveled distance, is constructed on a one-parametric family of closed flat constraints with four axes of symmetry. We discover 2π -periodic functions that differ from the classical trigonometric functions by the sign of curvature at every point of their existence. The asymptotic 2³ -periodic functions are computed and applied to the problem of motion of a material point along a closed flat-ribbed surface and to the modeling of kinematic perturbations of the bearing platforms of solid bodies.