Discontinuity, Nonlinearity, and Complexity
Integrability of a Time Dependent Coupled Harmonic Oscillator in Higher Dimensions
Discontinuity, Nonlinearity, and Complexity 7(1) (2018) 8194  DOI:10.5890/DNC.2018.03.007
Ram Mehar Singh$^{1}$, S B Bhardwaj$^{2}$, Kushal Sharma$^{3}$, Richa Rani$^{2}$, Fakir Chand$^{2}$, Anand Malik$^{4}$
$^{1}$ Department of Physics, Chaudhary Devi Lal University Sirsa125055, India
$^{2}$ Department of Physics, Kurukshetra University Kurukshetra136119, India
$^{3}$ Department of Mathematics, National Institute of Technology, Hamirpur177005, India
$^{4}$ Department of Physics, Chaudhary Bansi Lal University, Bhiwani127021, India
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Abstract
Within the frame work of extended complex phase space characterized by x = x1 + ip4,y = x2 + ip5,z = x3 + ip6, px = p1 + ix4, py = p2 + ix5 and pz = p3 +ix6, we investigate the exact dynamical invariant for a coupled harmonic system in three dimensions. For this purpose Liealgebraic method is employed and the invariant obtained in this work may play an important role in reducing the order of differential equations, solution of Cauchy system and to check the accuracy of a numerical simulation.
Acknowledgments
The authors are thankful to the learned referees for several useful comments which helped in considerably improving and finetuning some of the ideas in the original version of the paper.
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