本文探討移動之集電弓與電車線系統在垂直方向之動態互制特性。文中假設電車線系統中之懸臂組桿件及纜線為尤拉樑，吊掛線和斜吊線假設為單向彈簧，並將穩定臂模擬為一剛體。集電弓系統模擬成由三個質量、彈簧與阻尼組成之三個自由度系統，集電舟之彈性模擬成一彈簧，並連接一個虛擬的質量塊當作與接觸線保持接觸之滑塊。此文利用牛頓第二定律與有限元素法得到集電弓與電車線系統之離散化運動方程式，之後再組合成電車線/集電弓系統之運動方程式。接著，令虛擬的質量塊與接觸線的接觸點位移相等作為拘束條件，再利用多體動力學與拉格朗日乘數，結合修改的紐馬克數值積分法，以求得電車線/集電弓系統在每個時刻之動態響應。

This paper explores the dynamic intermodulation characteristics of the mobile pantograph and trolley line system in the vertical direction. It is assumed that the cantilever set rods and cables in the trolley line system are yello beams, the suspension line and the diagonal suspension line are assumed to be one-way springs, and the stabilizing arm is simulated as a rigid body. The pantograph system is modeled as a three-degree-of-freedom system consisting of three masses, a spring and a damping. The elasticity of the collector boat is modeled as a spring and connected to a virtual mass as a slider that remains in contact with the contact line. In this paper, Newton's second law and finite element method are used to obtain the discretization equations of the pantograph and tram line system, and then combined into the equation of motion of the tram line/collector system. Then, the displacement point of the virtual mass block and the contact line is equalized as a constraint condition, and the multi-body dynamics and the Lagrangian multiplier are combined, and the modified Newmark numerical integration method is used to obtain the trolley line/collection. The dynamic response of the bow system at each moment.

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