On the small-amplitude approximation to the differential equation x¨+(1+x˙2)x=0

摘要

We obtain the small-amplitude expansion for the period of the nonlinear oscillator x¨+(1+x˙2)x=0 with the initial conditions x(0)=A and x˙(0)=0, calculate its radius of convergence and show that the inverted perturbation series appears to converge smoothly from below.