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Русская версия

**Alexander V. Bratishchev**

Don State Technical University,

Professor of Applied Mathematics Department ,

Rostov-on-Don, Gagarin sq.,1

In this paper, we study the free movement on the horizontal plane of a platform with a spherical pendulum fixed in the center of mass. This system is considered as a system of two stationarily connected material points, one of which moves in the plane. The subsystem of differential equations describing the motion of the platform is integrated explicitly and the solution is a function of the variables describing the motion of this pendulum relative to the platform. In turn, in the system of fourth-order equations of motion of the pendulum relative to the platform, an independent autonomous subsystem of third-order equations is distinguished. A phase portrait of the latter system is constructed. This allowed us to give a complete description of the movement of the "Мobile platform with a pendulum" system at any of its initial states. The relationship in quadratures between the angular phase coordinates of the points of the trajectories of the system is established.

- cart
- equation of motion
- phase portrait
- platform
- spherical pendulum

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