Abstract
It is proved that conditionally periodical and chaotic paths of a system of connected mathematical pendulums exist for considerable ratios of the masses
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REFERENCES
A. A. Martynyuk and N. V. Nikitina, “Estimating the boundary of the domain of aperiodic motions,” Prikl. Mekh., 33, No. 12, 89–95 (1997).
V. K. Mel'nikov, “Stability of a center under periodic disturbances,” Tr. Moskovskogo Obshch., No. 12, 3–52 (1963).
V. Moauro and P. Negrini, “Chaotic paths of a double-link mathematical pendulum,” Prikl. Mat. Mekh., 62, No. 5, 892–895 (1998).
V. V. Nemytskii and V. V. Stepanov, The Qualitative Theory of Differential Equations [in Russian], Gostekhteorizdat, Moscow (1949).
V. I. Poddubnyi, Yu. E. Shamarin, D. A. Chernenko, and L. S. Astakhov, Dynamics of Underwater Towed Systems [in Russian], St.-Petersburg, Sudostroenie (1995).
A. M. Samoilenko, Elements of the Mathematical Theory of Multifrequency Vibrations. Invariant Tori [in Russian], Nauka, Moscow (1987).
P. Holmes and F. C. Moon, “Strange attractors and chaos in nonlinear mechanics,” Trans. ASME, J. Mech., 50, 1021–1032 (1983).
A. A. Martynyuk and N. V. Nikitina, “Dynamic principle of symmetry,” Int. Appl. Mech., 34, No. 11, 1158–1164 (1998).
A. A. Martynyuk and N. V. Nikitina, “The theory of motion of a double mathematical pendulum,” Int. Appl. Mech., 36, No. 9, 1252–1258 (2000).
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Martynyuk, A.A., Nikitina, N.V. Regular and Chaotic Motions of Mathematical Pendulums. International Applied Mechanics 37, 407–413 (2001). https://doi.org/10.1023/A:1011340116942
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DOI: https://doi.org/10.1023/A:1011340116942