A system of ideal polytropic gas equations written in the Lagrangian coordinates is considered on a uniformly rotating plane. For this system the first integrals corresponding to motions with uniform deformation are found. It is shown that, if the adiabatic index is equal to two, the original system consisting of four second-order nonlinear ordinary differential equations can be reduced to a single first-order equation and the solution can be found as a time function. The behavior of this solution is analyzed near equilibrium positions.

中文翻译：

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旋转平面上气体动力学方程解的性质：一致变形运动的情况

在均匀旋转的平面上考虑以拉格朗日坐标编写的理想多变气体方程组。对于该系统，找到与具有均匀变形的运动相对应的第一积分。结果表明，如果绝热指数等于2，则由四个二阶非线性常微分方程组成的原始系统可以简化为一个一阶方程，并且可以将其解作为时间函数。在平衡位置附近分析此解决方案的行为。