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Journal of Vibration Testing and System Dynamics 10(1) (2026) 83--104 | DOI:10.5890/JVTSD.2026.03.005

Albert C. J. Luo, Tianji Ma

Department of Mechanical and Mechatronics Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA

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Abstract

In this paper, impulsive periodic motions to the corresponding homoclinic orbits in an impulsively forced pendulum are obtained through the implicit mapping method. The periodic motions in the impulsive pendulum are determined from the specific mapping structure, and the corresponding stability and bifurcation analysis of the impulsive periodic motions are carried out. The bifurcation trees of the impulsive periodic motions to the impulsive homoclinic orbits are presented. The saddle-node and period-doubling bifurcations are obtained, and the impulsive homoclinic orbits are also achieved. The impulsive homoclinic orbits are relative to the corresponding impulsive periodic motions, which are called the homoclinic bifurcations of the impulsive periodic motions. The impulsive periodic motions and impulsive homoclinic orbits of the impulsive forced pendulum are illustrated for a better understanding of impulsive periodic motions in the impulsively forced pendulum. The infinite impulsive homoclinic orbits related all impulsive periodic motions can be found.

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