Abstract:
We find first integrals for the system of ideal polytropic gas dynamics on a uniformly rotating plane in Lagrangian coordinates, which correspond to the motion with uniform deformation. We show that if the adiabatic exponent $\gamma=2$, then the initial system of four second-order nonlinear ordinary differential equations can be reduced to one first-order equation and its solution can be found as a function of time. The behavior of the solution near equilibria is analyzed.
Key words:two-dimensional ideal polytropic gas equations, motion with uniform deformation, equilibria, exact solutions.
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