These results are illustrated and supported by simulations for different values of the parameters.
📌 3 Key Takeaways
🎯
Objective & Hypothesis:In this study, we consider spring-mass systems subjected to piecewise constant forces.
📊
Key Findings & Data:TheFloquet multipliers are taken into account for the stability analysis [3].
💡
Conclusion & Impact:These results are illustrated and supported by simulations for different values of the parameters.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Generalized piecewise constant forces · spring-mass system · stability and periodic solutions
Abstract
In this study, we consider spring-mass systems subjected to piecewise constant forces. We investigate sufficient conditions for the existence of periodic solutions of homogeneous and nonhomogeneous damped spring-mass systems with the help of the Floquet theory. In addition to determining conditions for the existence of periodic solutions, stability analysis is performed for the solutions of the homogeneous system. TheFloquet multipliers are taken into account for the stability analysis [3]. The results are stated in terms of the parameters of the systems. These results are illustrated and supported by simulations for different values of the parameters.
ARUĞASLAN, D., CENGİZ, N. (2022). Existence of periodic solutions for a mechanical system with piecewise constant forces. Hacettepe Journal of Mathematics and Statistics, Cilt: 47 - Sayı: 3, 521–538. https://ajindex.com/articles/529843
Aftabizadeh, A.R., Wiener, J. and Xu, J.-M. Oscillatory and periodic solutions of delay differential equations with piecewise constant argument, Proc. Amer. Math. Soc. 99, 673 679, 1987.
Akhmet, M.U. Integral manifolds of differential equations with piecewise constant argument of generalized type, Nonlinear Anal. 66, 367383, 2007.
Akhmet, M.U. On the integral manifolds of the differential equations with piecewise constant argument of generalized type, Proceedings of the Conference on Dierential and Dierence Equations at the Florida Institute of Technology, August 1-5, 2005,
Melbourne, Florida, Editors: R.P. Agarval and K. Perera, Hindawi Publishing Corporation, 1120, 2006.
Akhmet, M.U. Quasilinear retarded differential equations with functional dependence on piecewise constant argument, Communications On Pure And Applied Analysis 13 (2), 929 947, 2014.
Akhmet, M.U. Stability of differential equations with piecewise constant arguments of gen- eralized type, Nonlinear Anal. 68, 794803, 2008.
Akhmet, M.U. and Aru§aslan, D. Lyapunov-Razumikhin method for differential equations with piecewise constant argument, Discrete and Continuous Dynamical Systems, Series A 25 (2), 457466, 2009.
Akhmet, M.U., Aru§aslan, D. and Liu, X. Permanence of nonautonomous ratio-dependent predator-prey systems with piecewise constant argument of generalized type, Dynamics of Continuous Discrete and Impulsive Systems Series A. Mathematical Analysis 15 (1), 3751, 2008.
Akhmet, M.U., Aru§aslan, D. and Ylmaz, E. Stability analysis of recurrent neural networks with piecewise constant argument of generalized type, Neural Networks 23, 805811, 2010.
Akhmet, M.U., Aru§aslan, D. and Ylmaz, E. Stability in cellular neural networks with a piecewise constant argument, Journal of Computational and Applied Mathematics 233, 23652373, 2010.
Akhmet, M.U., Öktem, H., Pickl, S.W. and Weber, G.-W. An anticipatory extension of Malthusian model, CASYS'05-Seventh International Conference, AIP Conference Proceedings 839, 260264, 2006.
Busenberg, S. and Cooke, K.L. Models of vertically transmitted diseases with sequential- continuous dynamics, Nonlinear Phenomena in Mathematical Sciences, Academic Press, New York, 179187, 1982.
Chiu, K.-S., Pinto, M. Periodic solutions of differential equations with a general piecewise constant argument and applications, Electron. J. Qual. Theory Dier.