volume | PIER Journals

Abstract

In this paper, jerk function for a transient process of RL circuit is investigated. Some new concepts such as time rate of change of induced emf, time rate of change of displacement current, and Appell function have been introduced for the first time in electromagnetic jerky dynamics. The problems on Appell function of several simple models in electromagnetic jerky dynamics are discussed. In the last conclusions and remarks are also presented.

1. Schot, S. H., "Jerk: The time rate of change of acceleration," Am. J. Phys., Vol. 46, 1090-1094, 1978.
doi:10.1119/1.11504

2. Sandin, T. R., "The jerk," The Physics Teacher,, Vol. 28, 36-40, 1990.
doi:10.1119/1.2342925

3. Linz, S. J., "Nonlinear dynamical models and jerky motion," Am. J. Phys., Vol. 65, 523-526, 1997.
doi:10.1119/1.18594

4. Sprott, J. C., "Some simple chaotic jerk function," Am. J. Phys., Vol. 65, 537-543, 1997.
doi:10.1119/1.18585

5. VonBaeyer, H. C., "All shook up: The jerk, an old-fashioned tools of physics, find new applications in the theory chaos," The Sciences, Vol. 38, 12-14, 1998.

6. Ma, S. J., M. P. Liu, and P. T. Huang, "The form of three-order Lagrangian equation in relative motion," Chin. Phys., Vol. 14, 244-246, 2005.
doi:10.1088/1009-1963/14/2/004

7. Ma, S. J., W. G. Ge, and P. T. Huang, "The three-order Lagrangian equation for mechanical systems of variable mass," Chin. Phys., Vol. 14, 879-881, 2005.
doi:10.1088/1009-1963/14/5/003

8. Ma, S. J., X. H. Yang, and R. Yang, "Noether symmetry of three-order Lagrangian equations," Commun. Theor. Phys., Vol. 46, 309-312, 2006.
doi:10.1088/0253-6102/46/2/026

9. Ma, S. J., X. H. Yang, R. Yang, and P. T. Huang, "Lie symmetry and conserved quantity of three-order Lagrangian equations for non-conserved mechanical system," Commun. Theor. Phys., Vol. 45, 350-352, 2006.
doi:10.1088/0253-6102/45/2/031

10. Hamel, G., Theoretische Mechanik, Springer-Verlag, Berlin, 1949.

11. Linz, S. J., "Newtonian jerky dynamics: Some general properties," Am. J. Phys., Vol. 66, 1109-1114, 1998.
doi:10.1119/1.19052

12. Chlouverakis, K. E. and J. C. Sprott, "Chaotic hyperjerk system," Chaos, Solitons and Fractals, Vol. 28, 739-747, 2006.
doi:10.1016/j.chaos.2005.08.019

13. Linz, S. J., "On hyperjerk systems," Chaos, Solitons and Fractals, Vol. 37, 741-747, 2008.
doi:10.1016/j.chaos.2006.09.059

14. Appell, P., Traite de Mecanique Rationnelle II, Gauthier-Villars, Paris, 1904.

15. Pars, L. A., A Treatise on Analytical Dynamics, Heinemann, London, 1965.

16. Whittaker, E. T., A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge Univ. Press, Cambridge, 1937.

17. Gottlieb, H. P. W., "Harmonic balance approach to periodic solutions of non-linear jerk equations," J. Sound. Vib., Vol. 271, 671-683, 2004.
doi:10.1016/S0022-460X(03)00299-2

18. Gottlieb, H. P. W., "Harmonic balance approach to limit cycles or non-linear jerk equations," J. Sound. Vib., Vol. 297, 243-250, 2006.
doi:10.1016/j.jsv.2006.03.047

19. Linz, S. J., "No-chaos criteria for certain jerky dynamics," Phys. Lett. A, Vol. 275, 204-210, 2000.
doi:10.1016/S0375-9601(00)00576-4

20. Sprott, J. C. and S. J. Linz, "Algebraically simple chaotic flows," Int. J. Chaos Theory. Appl., Vol. 5, 3-22, 2000.

21. Patidar, V. and K. K. Sud, "Bifurcation and chaos in simple jerk dynamical systems," Pramana-J. Phys., Vol. 64, 75-93, 2005.
doi:10.1007/BF02704532

Dr. Xue-Xiang Xu

Dr. Shan-Jun Ma

Dr. Pei-tian Huang