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Cylinder on an incline as a fold catastrophe system. (English) Zbl 1056.70002

Summary: The motion of a cylinder on an inclined plane, acted upon by a torque along its axis, is studied theoretically and experimentally. It is shown that the potential for the centre-of-mass exhibits the features of a fold catastrophe potential, the control parameter being related to the strength of the torque. This parameter determines whether or not the system experiences stable equilibrium positions. If it does, depending on the initial conditions, it may perform oscillations around an equilibrium position, or it may cross a no-return point and roll down. A cylinder with a magnet inside, placed on the inclined plane in a region where a uniform magnetic field is present, is a real example of such a system. We constructed that system and report the data obtained in a set of experiments.

MSC:

70E18 Motion of a rigid body in contact with a solid surface
70-05 Experimental work for problems pertaining to mechanics of particles and systems
78A55 Technical applications of optics and electromagnetic theory
58K35 Catastrophe theory
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