On the dynamics of cranes, or spherical pendula with moving supports
作者： R.M. Ghigliazza , P. Holmes
DOI: 10.1016/S0020-7462(01)00141-X
关键词: Massless particle 、 Angular momentum 、 Mathematics 、 Equations of motion 、 Classical mechanics 、 Constant speed 、 Integrable system 、 Tower crane 、 Point particle 、 Hamiltonian (quantum mechanics)
摘要: We consider the dynamics of a tower crane: point mass suspended by light cable (itself assumed massless) from horizontally moving support. derive general equations motion, and analyse two cases in detail: linearly accelerating support, support describing circle at constant speed. show that former system remains completely integrable, spite fact energy is no longer conserved. In second case, while Hamiltonian conserved, there analogue angular momentum conservation appears to be non-integrable. find steadily rotating solutions, discuss their stability bifurcations, provide partial characterisation global orbit structures.
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sci-hub.se 参考文章(20)
John Guckenheimer, Philip Holmes, M. Slemrod, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields ,(1983)
Philip Holmes, Periodic, nonperiodic and irregular motions in a Hamiltonian system Rocky Mountain Journal of Mathematics. ,vol. 10, pp. 679- 694 ,(1980) , 10.1216/RMJ-1980-10-4-679
IUTAM Symposium on Recent Developments in Non-linear Oscillations of Mechanical Systems Springer Netherlands. ,(2000) , 10.1007/978-94-011-4150-5
Vladimir Igorevich Arnold, Mathematical methods of classical mechanics Graduate texts in mathematics. ,(1978)
Frederic Howell Miller, Partial Differential Equations ,(1941)
Daniel Edwin Rutherford, Classical Mechanics ,(1951)
T.E. Schellin, T. Jiang, C. Östergaard, Response analysis and operating limits of crane ships Journal of Ship Research. ,vol. 37, pp. 225- 238 ,(1993) , 10.5957/JSR.1993.37.3.225
Katrin Ellermann, Edwin Kreuzer, Moored Crane Vessels in Regular Waves IUTAM Symposium on Theoretical and Numerical Methods in Continuum Mechanics of Porous Materials. pp. 105- 113 ,(2000) , 10.1007/978-94-011-4150-5_11
Ioannis T. Georgiou, On the Global Geometric Structure of the Dynamics of the Elastic Pendulum Nonlinear Dynamics. ,vol. 18, pp. 51- 68 ,(1999) , 10.1023/A:1008356204490
Martin Golubitsky, Ian Stewart, Jerrold E. Marsden, Michael Dellnitz, The constrained Liapunov-Schmidt procedure and periodic orbits American Mathematical Society. ,(1995)