PERIODIC ORBIT OF THE PENDULUM WITH A SMALL NONLINEAR DAMPING

Minhua Cheng; Chengzhi Li

doi:10.11948/2018.649

2018 Volume 8 Issue 2

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Minhua Cheng, Chengzhi Li. PERIODIC ORBIT OF THE PENDULUM WITH A SMALL NONLINEAR DAMPING[J]. Journal of Applied Analysis & Computation, 2018, 8(2): 649-654. doi: 10.11948/2018.649

Citation:

Minhua Cheng, Chengzhi Li. PERIODIC ORBIT OF THE PENDULUM WITH A SMALL NONLINEAR DAMPING[J]. Journal of Applied Analysis & Computation, 2018, 8(2): 649-654. doi: 10.11948/2018.649

PERIODIC ORBIT OF THE PENDULUM WITH A SMALL NONLINEAR DAMPING

Minhua Cheng¹,
Chengzhi Li^1,2

1 School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China;
2 School of Mathematical Sciences, Peking University, Beijing 100871, China

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Abstract

Abstract

We study the pendulum with a small nonlinear damping, which can be expressed by a Hamiltonian system with a small perturbation. We prove that a unique periodic orbit exists for any initial position between the equilibrium point and the heteroclinic orbit of the unperturbed system, depending on the choice of the bifurcation parameter in the damping. The main tools are bifurcation theory and Abelian integral technique, as well as the Zhang's uniqueness theorem on Liénard equations.
- Periodic orbits /
- pendulum with a nonlinear damping /
- bifurcation /
- Abelian integrals
MSC: 34C07;34C08;37G15

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References

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