The motion of a point mass on the surface of a smooth funnel |
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| Authors: | A.P. Blinov |
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| Affiliation: | 1. School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, China;2. College of Engineering, Department of Mathematics and Computer Sciences, University of Exeter, Exeter, Devon, United Kingdom;1. School of Science, Dalian Maritime University, Dalian, Liaoning 116026, PR China;2. School of Microelectronics, Dalian University of Technology, Dalian, Liaoning 116024, PR China;1. Faculty of Materials Science and Chemistry, China University of Geosciences, 388 Lumo Road, Wuhan, Hubei, 430074, China;2. Engineering Research Center of Nano-Geomaterials of Ministry of Education, Faculty of Materials Science and Chemistry, China University of Geosciences, 388 Lumo Road, Wuhan, Hubei, 430074, China |
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| Abstract: | The motion of a point mass on a smooth concave surface (a funnel) under the action of a gravitational force is considered. The equations of motion are reduced to a form to which Lyapunov's theorem on the representation of the solution in the form of power series in the initial conditions, which converge absolutely in a finite region of phase space is applied. In the non-local formulation of the problem, a procedure is described for estimating the libration periods, based on an analysis of geometric forms. A bilateral estimate of the region of possible motion of the point is given for rotational-type motions, when the funnel is a surface of revolution. |
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