Hybrid journal (It can contain Open Access articles) ISSN (Print) 1752-2862 - ISSN (Online) 1752-2870 Published by Inderscience Publishers[447 journals]

Authors:Nita H. Shah, Mahesh A. Yeolekar Pages: 235 - 246 Abstract: The motion of a biped robot can be explained by a set of nonlinear ordinary differential equations. In this paper, we investigate the linearised form of a system of nonlinear ordinary differential equations with impulse effect which modelled a simple planer biped robot without knee. It demonstrated the periodic walking of biped robot in a sagittal plane in absence of external forces except gravity. This paper explains the bifurcation study for the system of biped robot with respect to the bifurcation parameters, mass and length. The results exhibit that the stable symmetric gait leads to chaotic gait by the continuous change in the values of parameters. We observed that the symmetric gaits of robot are more responsive for the values of length of legs than the values of masses of robot. Keywords: Biped robot; limit cycle walking; passive dynamic walking; Poincare map; orbital stability; bifurcation diagram Citation: International Journal of Applied Nonlinear Science, Vol. 2, No. 4 (2016) pp. 235 - 246 PubDate: 2017-08-14T23:20:50-05:00 DOI: 10.1504/IJANS.2016.085798 Issue No:Vol. 2, No. 4 (2017)

Authors:Bhawna Tandon, Shiv Narayan, Jagdish Kumar Pages: 247 - 257 Abstract: This study proposes a feedback linearisation based on the back-stepping method to design a nonlinear controller with a goal of improving both steady state and transient stability of a magnetic levitation system. The feedback linearisation based on back-stepping technique is the combination of the two techniques mentioned i.e. feedback linearisation and backstepping. It uses backstepping design process, designs a sequence of 'virtual' systems of relative degree one, reduces the relative degree by one by choosing a 'virtual' input, achieves passivity with respect to a 'virtual output', and the last 'virtual output' is used to close feedback loop. Unlike the direct feedback linearisation method, the proposed method does not require a linear controller. Moreover, there is no need to know the exact nonlinear model of the system. Back stepping process of the controller guarantees its robustness against disturbances and uncertainties. Keywords: backstepping technique; feedback linearisation; nonlinear control; magnetic levitation system; MLS Citation: International Journal of Applied Nonlinear Science, Vol. 2, No. 4 (2016) pp. 247 - 257 PubDate: 2017-08-14T23:20:50-05:00 DOI: 10.1504/IJANS.2016.085802 Issue No:Vol. 2, No. 4 (2017)

Authors:Shwet Nisha, Pradip K. Parida Pages: 258 - 269 Abstract: In this paper, we have developed an improved regula falsi method of order four for finding simple roots of nonlinear equations f(x) = 0, where f : [a; b] ⊂ R → R is a given continuously differentiable function. This is done by combining a Newton-like method of order four to solve f(x) = 0 and the usual regula-falsi method. Convergence analysis for the method has been given in this paper. Finally some numerical examples are presented and comparison has been made with existing results. Keywords: nonlinear equations; order of convergence; regula-falsi method; Newton-like methods Citation: International Journal of Applied Nonlinear Science, Vol. 2, No. 4 (2016) pp. 258 - 269 PubDate: 2017-08-14T23:20:50-05:00 DOI: 10.1504/IJANS.2016.085803 Issue No:Vol. 2, No. 4 (2017)

Authors:Najeeb Alam Khan, Chein-Shan Liu, Fatima Riaz Pages: 290 - 310 Abstract: In this paper, a novel multiple-scale polynomial-Fourier-series method (PFSM) is developed to be used in the data interpolation, in which the multiple-scale Rk can be determined exactly and optimally in terms of the data nodes. For solving the nonlinear Duffing equation, an optimally scaled harmonic balance method (OSHB) is derived, which is better than the classic harmonic balance method (HB). In terms of the OSHB, the periodic solutions of the Duffing oscillator, and reconstruction of the frequency response curves, which exhibit a hysteresis within which the multiple solutions can happen in an interval of frequency near to the resonant frequency can be precisely solved. The PFSM is further adapted to solve the initial value problem of the Duffing equation, and the periodic solution can be obtained more accurately than the HB. The proposed method has also been tested to solve the boundary value problem and the initial value problem of some nonlinear ordinary differential equations (ODEs). The conclusion can be drawn that the present OSHB and PFSM are effective to solve nonlinear ODEs, including the nonlinear Duffing equation as a demonstrative example. Keywords: Duffing equation; multiple-scale polynomial Fourier-series interpolation; harmonic balance method; optimally scaled harmonic balance method; OSHB; optimally scaled polynomial-Fourier-series method; PFSM Citation: International Journal of Applied Nonlinear Science, Vol. 2, No. 4 (2016) pp. 290 - 310 PubDate: 2017-08-14T23:20:50-05:00 DOI: 10.1504/IJANS.2016.085806 Issue No:Vol. 2, No. 4 (2017)

Authors:HÃ¼seyin Budak, Mehmet Zeki Sarikaya Pages: 311 - 327 Abstract: In this paper, a companion of trapezoid inequality for functions of two independent variables with bounded variation is established and some applications for general cubature formula are given. Keywords: function of bounded variation; Ostrowski type inequalities; Riemann-Stieltjes integrals; cubature formula Citation: International Journal of Applied Nonlinear Science, Vol. 2, No. 4 (2016) pp. 311 - 327 PubDate: 2017-08-14T23:20:50-05:00 DOI: 10.1504/IJANS.2016.085807 Issue No:Vol. 2, No. 4 (2017)