Electron. J. Differential Equations, Vol. 2017 (2017), No. 40, pp. 1-10.

Periodic oscillations of the relativistic pendulum with friction

Qihuai Liu, Lukai Huang, Guirong Jiang

Abstract:
We consider the existence and multiplicity of periodic oscillations for the forced pendulum model with relativistic effects by using the Poincare-Miranda theorem. Some detailed information about the bound for the period of forcing term is obtained. To support our analytical work, we also consider a forced pendulum oscillator with the special force $\gamma_0\sin(\omega t)$ including a sufficiently small parameter. The result shows us that for all $\omega\in(0,+\infty)$, there exists a $2\pi/\omega$ periodic solution under our settings.

Submitted April 6, 2016. Published February 6, 2017.
Math Subject Classifications: 34B15.
Key Words: Relativistic pendulum; Poincare-Miranda theorem; averaging; periodic solutions.

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Qihuai Liu
School of Mathematics and Computing Sciences
Guilin University of Electronic Technology
Guilin 541002, China
email: qhuailiu@gmail.com
Lukai Huang
School of Mathematics and Computing Sciences
Guilin University of Electronic Technology
Guilin 541002, China
email: 756060523@qq.com
Guirong Jiang
School of Mathematics and Computing Sciences
Guilin University of Electronic Technology
Guilin 541002, China
email: grjiang9@163.com

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