在本研究中，首先針對呼拉圈行為進行描述並定義，進一步提出呼拉圈系統的架構，呼拉圈系統包含主質量與相對於主質量旋轉的自由質量，藉著主質量的往復運動帶動自由質量的旋轉運動，如同人搖呼拉圈的動態概念，主質量相當於人體，自由質量相當於呼拉圈。
考慮系統受到脈衝力作用，以能量法建立系統的非線性運動方程式，經由動態分析去瞭解系統參數與呼拉圈行為之間的關聯性。再利用能表達呼拉圈行為的近似解析解，透過穩定度分析去評估解存在的可能性，並藉著數值模擬去驗證穩定度分析結果的正確性，並輔以相平面圖與Poincaré截面圖進行動態響應分析。從結果可以發現到，選擇適當的系統初始條件，呼拉圈行為的發生是可預期的，並且可以應用於旋轉式微型發電機的設計。

In this thesis, the concept and definition of hula-hoop motion will be introduced. The hula-hoop system is constructed simply by a main mass and a free-moving mass. By mimicking the motion characteristics of the hula-hoop, which is commonly regarded as the circular oscillations where a ring spins around a moving human body. The main mass that performs reciprocating motion is considered as the human body while the free-moving mass that rotates around the main mass simulates the ring.
Considering the impulsive excitation as the external force, the governing nonlinear equations are first formulated based upon Lagrange’s equation. Then, a thorough dynamic analysis is performed to understand the relation between the varied system parameters and the chance of occurrence of hula-hoop motion. The possibility of existence of the approximate analytical solutions can be evaluated by stability analysis. The numerical simulation is also performed by using direct integration method to verify the aforementioned qualitative analysis. Finally, Phase plane and Poincaré section are used to analyze the dynamic response. On the basis of the obtained results, the design guidelines for initial conditions to ensure the occurrence of hula-hoop motions are distilled and can be applied to the micro-generator.

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