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

Francisco M. Fernández

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arXiv · 0907.3505

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

Francisco M. Fernández

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Abstract

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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BibTeX RIS

Francisco M. Fernández. 2010-01-13. On the small--amplitude approximation to the differential equation $\ddot{x}+(1+\dot{x}^{2})x=0$. https://arxiv.org/abs/0907.3505

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