关于动力方程的建立及其相关证明之历史探析:从泊松到斯托克斯

Historical Research on the Establishment of the Dynamical Equation and Its Associated Proofs:From Poisson to Stokes

通过建立动力方程来描述流体运动状态,是早期流体动力学发展历史中的重要目标。在伯努利、达朗贝尔、欧拉、拉格朗日等人的流体静力学工作基础上,泊松、柯西、斯托克斯等人给出了流体动力学中相对完整的方程,重要的是他们证明了动力方程在什么条件下是可积的重要定理。对欧拉给出的流体力学基本方程进一步完善,这为19世纪英国以斯托克斯为中心的流体动力学研究奠定了基础。追溯泊松、柯西、斯托克斯三人的数学思想方法,有助于我们更好地认识18世纪末到19世纪数学知识的认知和应用过程。

Describing the state of motion of a fluid by building dynamical equations was an important goal in the early history of fluid dynamics.Based on the foundation of hydrostatic studies by Bernoulli,D'Alembert,Euler,Lagrange and others,Poisson,Cauchy,Stokes and others gave relatively complete equations in fluid dynamics and,importantly,they proved important theorems on the conditions under which the dynamical equations are integrable.Their further refinement of the fundamental equations of fluid dynamics given by Euler laid the foundations for nineteenth century British research in fluid dynamics centered on Stokes.Tracing the mathematical approach to the thought of the trio of Poisson,Cauchy,and Stokes helps us to better understand the process of perception and application of mathematical knowledge from the late 18th to the 19th century.