Isochronicity of a class of piecewise continuous oscillators

Mañosas, Francesc; Torres, Pedro

doi:10.1090/S0002-9939-05-07873-1

Isochronicity of a class of piecewise continuous oscillators
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by Francesc Mañosas and Pedro J. Torres

Proc. Amer. Math. Soc. 133 (2005), 3027-3035

DOI: https://doi.org/10.1090/S0002-9939-05-07873-1

Published electronically: March 31, 2005

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Abstract:

Motivated by a classical pendulum clock model suggested by Andrade in 1920, we study the equation $\ddot x+g(x)\operatorname {sgn}{\dot x}+x=0$ and prove that for a nonlinear analytic $g$ the origin is never an isochronous focus or an isochronous center.

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