1. bookVolume 28 (2020): Issue 1 (March 2020)
Journal Details
License
Format
Journal
eISSN
1844-0835
First Published
17 May 2013
Publication timeframe
1 time per year
Languages
English
access type Open Access

Numerical aspects of two coupled harmonic oscillators

Published Online: 09 Apr 2020
Page range: 5 - 15
Received: 28 Jun 2019
Accepted: 26 Jul 2019
Journal Details
License
Format
Journal
eISSN
1844-0835
First Published
17 May 2013
Publication timeframe
1 time per year
Languages
English
Abstract

In this study an interesting symmetric linear system is considered. As a first step we obtain the Lagrangian of the system. Secondly, we derive the classical Euler- Lagrange equations of the system. Finally, numerical and analytic solution for these equations have been presented for some chosen initial conditions.

Keywords

MSC 2010

[1] J.B. Marion, S.T. Thornton, Classical Dynamics of Particles and Systems, 5th Edition, Brooks Cole (2003)Search in Google Scholar

[2] W. Greiner, Classical Mechanics, Systems of Particles and Hamiltonian Dynamics, Springer-Verlag Berlin Heidelberg (2010)Search in Google Scholar

[3] Goldstein H, Poole C P, and Safko J L, Classical Mechanics, 3rd edn. Addison Wesley (1980).Search in Google Scholar

[4] N.E. Martnez-Prez, C. Ramrez, On the Lagrangian description of dissipative systems, Journal of Mathematical Physics, 59 (3) (2018).10.1063/1.5004796Search in Google Scholar

[5] D.M. Gitman, V.G. Kupriyanov, Canonical quantization of so-called non-Lagrangian systems, European Physical Journal, 50 (3), (2007).10.1140/epjc/s10052-007-0230-xSearch in Google Scholar

[6] C.P. Pesce, The Application of Lagrange Equations to Mechanical Systems With Mass Explicitly Dependent on Position, Journal of Applied Mechanics. 70, (2007), 751-756.10.1115/1.1601249Search in Google Scholar

[7] D. Bala, Geometric Methods In Study Of The Stability Of Some Dynamical Systems, An. St. Univ. Ovidius Constanta, 17(3, (2009), 27-35.Search in Google Scholar

[8] M. Lupu, O. Florea, C. Lupu, The structural influence of the forces of the stability of dynamical systems, An. St. Univ. Ovidius Constanta 17(3), (2009), 159 - 169.Search in Google Scholar

[9] S. Vlase, M. Marin, A. Ochsner, ML Scutaru, Motion equation for a flexible one-dimensional element used in the dynamical analysis of a multibody system, Continuum Mechanics and Thermodynamics, 31(3), (2019), 715-724.10.1007/s00161-018-0722-ySearch in Google Scholar

[10] D. Dingy Xue, Y. Chen, System Simulation Techniques with MATLAB and Simulink, Wiley, (2013)Search in Google Scholar

[11] H. Klee, R. Allen, Simulation of Dynamic Systems with MATLAB and Simulink, CRC Press Taylor & Francis Group, (2011)Search in Google Scholar

[12] D. K. Chaturvedi, Modeling and Simulation of Systems Using MATLAB and Simulink, CRC Press Taylor & Francis Group, (2010)Search in Google Scholar

[13] O. Beucher, M. Weeks, Introduction to MATLAB and SIMULINK, A Project Approach, Third Edition (Engineering, Infinity Science Press LLC Hingham, Massachusetts New Delhi, (2006)Search in Google Scholar

[14] H-P Halvorsen, Introduction to Simulink, Faculty of Technology, Norway, http://www.academia.edu/9207393/Introduction_to_SimulinkSearch in Google Scholar

[15] Gh. Lupu, E.M. Craciun, E. Suliman, An Extension of Equilibrum Problem for the Plane Simple Pendulum, An. St. Univ. Ovidius Constanta, seria Matematica, 1, (1993), 141-145.Search in Google Scholar

[16] Gh. Lupu, A. Rabaea, E.M. Craciun, Theoretical Aspects Concerning Vibrations of Elastical Technological Systems, An. St. Univ. Ovidius Constanta, seria Matematica, 1, (1993), 133-139.Search in Google Scholar

[17] G. Groza, A-M Mitu, N. Pop, T. Sireteanu, Transverse vibrations analysis of a beam with degrading hysteretic behavior by using Euler-Bernoulli beam model, An. St. Univ. Ovidius Constanta, seria Matematica, 26(1), (2018), 125 - 139.10.2478/auom-2018-0008Search in Google Scholar

Recommended articles from Trend MD

Plan your remote conference with Sciendo