Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/2602
標題: 系統動力學動量公式推導過程之探討
On the derivation process of momentum equations in system dynamics
作者: 鄭自強
關鍵字: 系統動力學;動量公式;尤拉公式;伯努利公式;追蹤雷諾輸送公式
出版社: 機械工程學系
摘要: 
力學的發展從阿基米德、達文西、巴斯卡以降,到1687年牛頓發表“自然哲學的數學原理”開啟了動力分析的先河,其後系統動力學的理論架構也日趨成熟,在變質量系統動力領域也奠定了些許基礎,近年來更續有重大突破。系統動力學動量分析方法常使用追蹤分析法、區域分析法,或能量/動量綜合分析法,本文先以固體力學之拉繩/落繩問題為例,除說明追蹤動量分析及區域動量分析之殊途同歸性,並深入淺出探討能量/動量綜合分析方法中隨意假設無能損的狀態所造成之嚴重的錯誤,以及衝擊能損對於系統動力問題的深遠影響。而流體力學因其涉及非線性偏微分方程,雖經數百年的努力,其系統動力分析仍舊問題重重。因此本文隨後並探討由於不經意地假設無能損條件下,流體力學基本動量分析理論體系推導過程的錯誤,令人吃驚的是,這些歷史性、全面性的錯誤卻是緣於暗中強制假設流管之壁壓等於流線方向之壓力。即使是看來無懈可擊的純粹動力公式型態的尤拉/伯努利方程式,因遲早會遭遇縮/擴流管狀態,而當在此動力公式推導過程強令壁壓等於流向壓力,就是暗地強加無能損之假設,因而形成影響深遠的歷史性重大失誤。

The concept development of mechanics might start from Archimedes, Leonardo da Vinci, and Blaise Pascal. Later, Newton's “Philosophiae Naturalis: Principia of Mathematica” unveils the methodology of dynamics analysis. Subsequently, the theory of system dynamics gradually grows mature, and its infrastructures in dynamics of varied mass system are also preliminarily established. Continuously, there are some important relevant breakthroughs in recent years. Momentum analysis of system dynamics usually makes use of lagrangian method, eulerian method, or energy/momentum method. In this paper, we first take rope-lifting/falling problems as examples to illustrate the identity of lagrangian and eulerian methods. We also point out that serious mistakes can be resulted from arbitrary assumption of no-energy-loss in using energy/momentum method, and explain the crucial effect of impact energy loss in system dynamics. Since fluid mechanics involves nonlinear partial differential equation, thus even after several hundred years of endeavor, its analyses still remain problematic. In that light, later we will demonstrate that some deriving mistakes in the theoretic analysis of fluid mechanics are likewise due to an careless assumption of no-energy-loss condition. More Surprisingly, these historical and panoramic mistakes can be originated from the clandestinely forced assumption that the crosswise pressure equates the streamwise pressure in flow field. Since sooner or later, fluid element will encounter divergent/convergent conditions of streamtubes, then due to the said clandestinely forced assumption of crosswise pressure equalization, even the seemingly perfect dynamics forms of Euler/Bernoulli equations cannot help but fall into a far-reaching historical error in their deriving process.
URI: http://hdl.handle.net/11455/2602
Appears in Collections:機械工程學系所

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