# SOLUTION OF PARAMETRIZED RYAPOLOV EQUATION

Ryapolov's differential equation has many applications in various problems, e.g., computing plane engine trac-tive force necessary for achieving given speed and acceleration at the end of a runway. Parametrized Ryapolov equation and its solutions describe dependencies between parameters of motion of objects in liquids or gas re-gardless of constructional properties. The equation is solved for arbitrary values of parameter n that stands for the power of velocity proportional to resistance force. This allows to analytically compute parameters of complex objects moving at high speed. The solution for the case of resistance force proportional to third power of speed is explicitly written out. All computations are carefully spelled out, so that they are easy to comprehend for stu-dents and engineers.

**Authors:** V. A. Smirnova

**Direction:** Informatics, Computer Technologies And Control

**Keywords:** Parametrized Ryapolov equation, first integral, parametric solution

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