Double pendulum’s slow dynamics analysis

Authors

  • Ligia Munteanu Institute of Solid Mechanics, Romanian Academy, Bucharest
  • Marius Ionescu Institute of Solid Mechanics, Romanian Academy, Bucharest
  • Nicoleta Stan Institute of Solid Mechanics, Romanian Academy, Bucharest
  • Valerica Mosnegutu Institute of Solid Mechanics, Romanian Academy, Bucharest
  • Veturia Chiroiu Institute of Solid Mechanics, Romanian Academy, Bucharest

Keywords:

pendulum motion, Coulomb vibrations, slow dynamics

Abstract

By extending the analysis of the slow dynamics, the solutions of a double pendulum motion written as a linear superposition of Coulomb vibrations have broken symmetry concerning the driving excitation. The solutions allow a qualitative analysis not only of the quasi-periodic behavior but also of the chaotic behavior of the pendulum. The solutions permit understanding what causes an oscillation to lose its periodicity and hence become chaotic.

References

GUYER, R. A., JOHNSON, P. A., Slow dynamics, Physics Today, 52, 30, 1999.

JOHNSON, P. A., SUTIN, A., DARLING, T., Nonlinear, elastic wave slow dynamics in certain metals, in a sintered ceramic, and in cracked solids: a probe of atomic-scale mechanics, Los Alamos National Laboratory, Los Alamos, NM, USA, 1999.

MISHRA, R. S., MUKHERJEE, A. K., MURTY, K. L., eds., Creep Behavior of Advanced Materials for the 21st Century, Minerals Metals & Materials Society, 1999.

TenCATE, J. A., SMITH, E., GUYER, R. A., Universal slow dynamics in granular solids, Phys. Rev. Lett., 85, 5, pp. 1020-1024, 2000.

FISCHER, K. H., HERTZ, J. A., Spin Glasses, Cambridge University Press, Cambridge, 1991.

GUYER, R. A., McCALL, K. R., BOITNOTT, G., Hysteresis, Discrete Memory, and Nonlinear Wave Propagation in Rock: A New Paradigm, Phys. Rev., 74, 3491, 1995.

DEN ABEELE, K., JOHNSON, P. A., SUTIN, A., Nonlinear Wave Modulation Spectroscopy, Res. NonDestr. Eval., 12, 1, pp. 17-30, 2000.

FIELD, E. H., JOHNSON, P. A., BERESNEV, I., ZENG, Y., Nonlinear sediment response during the 1994 Northridge, Nature, 390, 599, 1997.

TOMA, I., Metoda echivalen?ei lineare ?i aplica?iile ei în mecanic?, Editura Tehnica, Bucuresti, 2008.

TOMA, I., The nonlinear pendulum from a LEM perspective, Research Trends in Mechanics, Editura Academiei, Bucuresti, eds. POPA, D., CHIROIU, V., TOMA, I., 1, pp. 395-422 2007.

TOMA, I., Metoda echivalentei lineare si aplicatiile ei, Editura Flores, Bucuresti, 1995.

TOMA, I., Specific LEM techniques for some polynomial dynamical systems, Topics in Applied Mechanics, Editura Academiei, eds. CHIROIU, V., SIRETEANU, T., 3, pp. 427-459, 2006.

TEODORESCU, P. P., CHIROIU, V., MUNTEANU, L., MOSNEGUTU, V., Solu?ii LEM pentru o problema Lotka-Volterra, Stiinta si Inginerie, X, 17, pp. 625-630, 2010.

CRACIUN, F., BETTUCCI, A., MOLINARI, E., PETRI, A., ALIPPI, A., Direct experimental observation of fracton mode patterns in one-dimensional Cantor composites, Phys. Rev. Lett., 68, 10, 1992.

ALIPPI, A., SHKERDIN, G., BERTTUCCI, A., CRACIUN, F., MOLINARI, E., PETRI, A., Threshold lowering for subharmonic generation in Cantor composite structures, Physica A, 1992.

ALIPPI, A., CRACIUN, F., MOLINARI, E., Stopband edges in the dispersion curves of Lamb waves propagating in piezoelectric periodical structures, Appl. Phys. Lett., 53, 19, 1988.

ALIPPI, A., Nonlinear acoustic propagation in piezoelectric crystals, Ferroelectrics, 42, pp. 109-116, 1982.

ZINCHUK, L. P., PODLIPENETS, A. N., Oscillation modes in a surface shear wave propagating through a regularly laminated electroelastic half-space, Prikl. Mech, 27, 8, pp. 49-54, 1991.

SAVIN, V. G., Distribution of stresses and displacements in a Love wave in a laminated half-space, Prikl. Mech, 9, 11, pp. 111-114, 1973.

CHIROIU, C., DELSANTO, P. P., SCALERANDI, M., CHIROIU, V., SIRETEANU, T., Subharmonic generation in piezoelectrics with Cantor-like structure, Journal of Physics D: Applied Physics, Institute of Physics Publishing, 34, 3, pp. 1579-1586, 2001.

MUNTEANU, L., DONESCU, S., Introduction to Soliton Theory: Applications to Mechanics, Book Series Fundamental Theories of Physics, 143, Kluwer Academic Publishers, 2004.

CHIROIU, V., CHIROIU, C., Probleme inverse în mecanic?, Editura Academiei, Bucharest, 2003.

Published

2024-04-21

Most read articles by the same author(s)

<< < 1 2 3 4 > >>