About fluctuation of oscillator with quadratic nonlinear stiffness

Abstract

In this work the free oscillations of the system with one degree of freedom provided by elastic force of the spring is proportional to the square of its deformation. Two forms of analytical solution of nonlinear differential equations were built. At first, the solution is expressed through elliptic cosine, and the second - in Ateb-function. A table for computing the values of these functions got and built in dimensionless coordinates schedules that simplify calculations oscillator movement in time. The formula for calculating period of oscillation  in the oscillator providing initial deviation from the equilibrium position or initial velosity (momentary impulse) are obtained. The examples of calculations using known tables incomplete elliptic integral of the first kind and using a table

Ateb-functions are shown.