The presented work deals with nonlinear dynamics of a three degree of freedom system with a spherical pendulum and a damper of the fractional type. Vibrations in the vicinity of the internal and external resonance are considered. The system consists of a block suspended from a linear spring and a fractional damper, and a spherical pendulum suspended from the block. The viscoelastic properties of the damper are described using the Caputo fractional derivative. The fractional derivative of an order of \(0 < \alpha \le 1\) is assumed. The impact of a fractional order derivative on the system with a spherical pendulum is studied. Time histories, the internal and external resonance, bifurcation diagrams, Poincaré maps and the Lyapunov exponents have been calculated for various orders of a fractional derivative. Chaotic motion has been found for some system parameters.

提出的工作涉及具有球摆和阻尼器的三自由度系统的非线性动力学。考虑内部和外部共振附近的振动。该系统由悬挂在线性弹簧和分数阻尼器上的滑块以及悬挂在滑块上的球形摆组成。使用Caputo分数导数描述了阻尼器的粘弹性。\（0 <\ alpha \ le 1 \）阶的分数导数假设。研究了分数阶导数对具有球摆的系统的影响。对于分数阶导数的各个阶次，已经计算了时间历史，内部和外部共振，分叉图，庞加莱图和Lyapunov指数。已发现某些系统参数的混沌运动。