On the small--amplitude approximation to the differential equation $\ddot{x}+(1+\dot{x}^{2})x=0$

Details On the small--amplitude approximation to the differential equation $\ddot{x}+(1+\dot{x}^{2})x=0$ On the small--amplitude approximation to the differential equation $\ddot{x}+(1+\dot{x}^{2})x=0$

2009-07-20

arxiv.org/abs/0907.3505v2

Physics

Mathematical Physics

Scientific paper

We obtain the radius of convergence of the small--amplitude approximation to
the period of the nonlinear oscillator $\ddot{x}+(1+\dot{x}^{2})x=0$ with the
initial conditions $x(0)=A$ and $\dot{x}(0)=0$ and show that the inverted
perturbation series appears to converge smoothly from below.

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