连续介质的相对论力学
Relativistic Mechanics of Continuous Media
摘要：
在这项工作中，我们研究连续介质的相对论力学的基本水平上使用显着协变的适当的时间程序。我们制定的运动方程和连续性（和本构方程），是任何计算的起点，关于连续介质。在无力极限下，恢复了标准的相对论方程，使这些方程可以看作是标准过程的推广。在无粘性流体的情况下，我们导出了类似于伯努利方程的方程。对于无旋流动，我们证明了速度场可以从一个潜在的。此外，如果流体是不可压缩的，则势必须服从达朗贝尔方程，因此问题被简化为求解具有特定边界条件的达朗贝尔方程（在空间和时间上）。这些解表明在不可压缩流体中存在光速声波（从以前的文献[19]中已知的结果）。放松约束，并允许流体成为线性可压缩的，人们可以推导出一个波动方程，从该方程可以再次计算声速。对于定常背景流，本文证明了在不可压缩和非相对论性的极限下，声速达到其正确的值。最后，粘度介绍，体积和剪切粘度常数的定义，我们制定的粘性流体的运动方程。
英文摘要：
In this work we study the relativistic mechanics of continuous media on a fundamental level using a manifestly covariant proper time procedure. We formulate equations of motion and continuity (and constitutive equations) that are the starting point for any calculations regarding continuous media. In the force free limit, the standard relativistic equations are regained, so that these equations can be regarded as a generalization of the standard procedure. In the case of an inviscid fluid we derive an analogue of the Bernoulli equations. For irrotational flow we prove that the velocity field can be derived from a potential. If, in addition, the fluid is incompressible, the potential must obey the d'Alembert equation, and thus the problem is reduced to solving the d'Alembert equation with specific boundary conditions (in both space and time). The solutions indicate the existence of light velocity sound waves in an incompressible fluid (a result known from previous literature [19]). Relaxing the constraints and allowing the fluid to become linearly compressible, one can derive a wave equation from which the sound velosity can again be computed. For a stationary background flow, it has been demonstrated that the sound velocity attains its corrrect values for the incompressible and non-relatvistic limits. Finally, viscosity is introduced, bulk and shear viscosity constants are defined, and we formulate equations for the motion of a viscous fluid.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
