标题： 300年振动弦争议的解决 显示英文标题

标题： Resolution of the 300-Year-Old Vibrating String Controversy

摘要： 关于著名的1D振动弦模型及其解的争议，被称为振动弦争议，贯穿整个1700年代，并涉及当时最杰出的一群科学家。 此后，该模型在两个多世纪内没有受到质疑。 在本研究中，证明了不仅这个300年的模型无法对应现实，而且在理论上也不完全合理。 开发了一个新的2D模型，去除了经典模型的所有假设。 结果是一对非线性偏微分方程，用于模拟有限1D弦的2D运动。 证明了一个定理，可用于从弦的初始形状确定初始位移函数。 新模型能够表示经典模型无法处理的初始条件。 它还允许初始非紧/非松的弦和自相交的形状。 经典模型和非紧的弦作为特殊情况出现。 证明了1D弦的纯横向运动只有在非常罕见的情况下才可能发生。 还提出了一个设定纯横向运动条件的定理。 提供了对有趣案例的数值研究，以支持新模型。 还进行了高速摄像机实验，其结果也支持新理论。 显示英文摘要

摘要： The dispute about the well-known 1D vibrating string model and its solutions, known as The Vibrating String Controversy, spanned the whole of 1700s and involved a group of the most eminent scientists of the time. After that, the model stood undisputed for over two centuries. In this study, it is shown that not only this 300-year-old model cannot correspond to reality, but it is theoretically not quite plausible, either. A new 2D model is developed removing all the assumptions of the classical model. The result is a pair of non-linear partial differential equations modeling 2D motions of a finite 1D string. A theorem that can be used to determine the initial displacement functions from the initial shape of the string is proven. The new model is capable of representing initial conditions that cannot be handled in the classical model. It also allows initially non-taut/non-slack strings and self-intersecting shapes. The classical model and the non-taut strings emerge as special limit cases. It is proven that pure transverse motions of a 1D string are possible only in very rare cases. A theorem that sets the conditions for pure transverse motions is also presented. Numerical studies of interesting cases are presented in support of the new model. High-speed camera experiments are also conducted, the results of which also support the new theory.