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On the derivation process of momentum equations in system dynamics
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.
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