Comments on the paper “On nonlinear dynamics behavior of an electro-mechanical pendulum excited by a nonideal motor and a chaos control taking into account parametric errors” published in this journal
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Electromechanical systems are an interesting type of coupled systems. The mutual influence between electromagnetic and mechanical subsystems characterizes coupling. Each subsystem affects the behaviour of the other. Typically, the dynamics of an electromechanical system is expressed by an initial value problem (IVP) that comprises a set of coupled differential equations involving electrical and mechanical variables, as for example, current and angle. This article discusses a hypothesis found in a recent paper published in this journal (“On nonlinear dynamics behavior of an electromechanical pendulum excited by a nonideal motor and a chaos control taking into account parametric errors”) and in some thesis. The hypothesis is that it is possible to consider the derivative of the current equal to zero in the IVP that gives the dynamics of an electromechanical system without changing the system dynamics. The hypothesis is based only on some parameter values and, also, does not depend on the electromechanical system being analysed. Apparently, it is a nice hypothesis since it simplifies the dynamics greatly. With the hypothesis, the number of equations in the IVP that gives the dynamics is reduced. The hypothesis results in a reduced system, a simplification of the complete one. However, the hypothesis contradicts itself and changes the dynamics. The reduced system does not represent the complete system, and, moreover, it decouples the electromagnetic and mechanical subsystems. The reduction eliminates the mutual interaction between the subsystems, i.e., eliminates the coupling. To highlight the problems of the reduction, self-contradiction and dynamical change, we analyse the effects of the hypothesis for a simple electromechanical system, a motor-cart system. For the chosen system, the equations of the two IVP, reduced and complete, are presented and numerical simulations are performed. Considering just the results of simulations of the reduced IVP, it is possible to verify the self-contradiction of the hypothesis made. Comparing the results of simulations of the reduced and complete IVPs, it is possible to see, immediately, the big difference between the two dynamics.
KeywordsCoupled systems Electromechanical systems Parametric excitation
This work was supported by the Brazilian Agencies CNPQ, CAPES and Faperj.
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Conflict of interest
The authors declare that they have no conflict of interest.
- 1.Avanço R (2015) Análise da dinâmica não-linear de pêndulos com excitação paramétrica por um mecanismo biela-manivela. Ph.D. thesis, USP-São Carlos, São Carlos, SP, BrazilGoogle Scholar
- 3.Belato D (2002) Análise não linear de sistemas dinâmicos holonômos não ideais. Ph.D. thesis, Unicamp, Campinas, SP, BrazilGoogle Scholar
- 5.Clerkin E, Sampaio R (2017) A bifurcation and symmetry discussion of the Sommerfeld effect. In: Proceedings of 14th international conference in dynamical systems theory and applications (dynamical systems theory and applications). Łódź, PolandGoogle Scholar
- 7.Dantas M, Sampaio R, Lima R (2015) Phase bifurcations in an electromechanical system. In: IUTAM symposium on analytical methods in nonlinear dynamics. IUTAM 2015, Frankfurt, GermanyGoogle Scholar
- 14.Lima R, Sampaio R (2012) Analysis of an electromechanic coupled system with embarked mass. Mecânica Comput XXXI:2709–2733Google Scholar
- 16.Lima R, Sampaio R (2018) Pitfalls in the dynamics of coupled electromechanical systems. In: Proceeding series of the Brazilian society of computational and applied mathematics (CNMAC 2018). Campinas, BrazilGoogle Scholar
- 17.Lima R, Sampaio R, Hagedorn P (2018) One alone makes no coupling. Mecánica Comput XXXVI(20):931–944Google Scholar
- 18.Manhães W, Sampaio R, Lima R, Hagedorn P (2019) Two coupling mechanisms compared by their Lagrangians. In: XVIII international symposium on dynamic problems of mechanics (DINAME 2019). Buzios, RJ, BrazilGoogle Scholar
- 19.Manhães W, Sampaio R, Lima R, Hagedorn P, Deü J (2018) Lagrangians for electromechanical systems. Mecánica Comput XXXVI(42):1911–1934Google Scholar