... at the contact points of rolling elements and races, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The numerical integration technique Newmark-β with the Newton–Raphson method is used to solve the nonlinear differential equations, iteratively. The effect of bearing running...

.... Methods Software , 6 ( 3 ), pp. 193 – 217 . 10.1080/10556789508805633 Newton method nonlinear differential equations nonlinear dynamical systems optimisation parameter estimation regression analysis deterministic optimization global optimization homotopy continuation measurement...

... 2011 22 07 2011 22 07 2011 Galerkin method Legendre polynomials nonlinear differential equations wave equations Legendre multiwavelet DGRLW equation Ritz method Galerkin method The damped generalized regularized long-wave (DGRLW) equation is a partial differential...

... catastrophic failures. 20 10 2009 02 07 2010 16 12 2010 16 12 2010 approximation theory closed loop systems discrete systems feedback linear systems nonlinear control systems nonlinear differential equations partial differential equations piezoelectric actuators plates...

... penalty function dynamical system fractional derivative Adomian decomposition method multistage strategy nonlinear differential equations nonlinear dynamical systems 25 11 2009 15 03 2010 20 10 2010 20 10 2010 2011 American Society of Mechanical Engineers ...

... trajectory, and then carry out the approximation of the Lyapunov exponents using techniques for linear problems. 27 05 2009 20 04 2010 27 09 2010 27 09 2010 approximation theory Jacobian matrices Lyapunov methods nonlinear differential equations vectors Lyapunov...

... ( a − b ) 2 + 2 k m ) 1 / 2 20 09 2008 12 05 2009 18 11 2009 18 11 2009 beams (structures) nonlinear differential equations vibrations nonlinear vibration two degrees of freedom analytical solution homotopy analysis method homotopy...

... in the form of uniformly convergent series is obtained. The same orbit is also obtained numerically by a technique enunciated by Magnitskii and Sidorov, reproducing the necessary important features. 21 10 2008 03 06 2009 18 11 2009 18 11 2009 chaos nonlinear differential equations...

... with an unbalanced motor of excitation with limited power supply. The control of motion and the attenuation of the Sommerfeld effect of the considered nonideal system are analyzed in this paper. The mathematical model of the system is represented by coupled nonlinear differential equations. The identification...

... provide a very detailed picture of the dynamics and the most likely states of the system can immediately be identified. chaos gears noise nonlinear differential equations probability stochastic processes stochastic differential equation probability density function gear dynamics path...

... physical systems for the study of their nonlinear dynamics ( 6 7 ). multiple time scales method normal form theory Duffing equation internal resonance spring-mass-pendulum system nonlinear differential equations nonlinear dynamical systems perturbation theory 26 11 2007 23...

... 2007 nonlinear differential equations parameter estimation time-varying systems NLTV systems parameter estimation Chebyshev spectral collocation Nonlinear ordinary differential equations with unknown parameters and general time-varying coefficients are encountered...

... ) for analyzing Duffing’s equation has been widely cited by researchers in the areas of nonlinear phenomena studies. Duffing’s equation investigated by Ueda ( 17 ) is for a typical nonlinear dynamic system governed by a second-order nonlinear differential equation in the following form: 25 x ̈ + k x...

... and temporal variations of tensile/compressive forces are considerably important. 15 09 2006 28 03 2007 bifurcation chaos elastodynamics nonlinear differential equations oscillations partial differential equations spatiotemporal phenomena vibrations wires inclined cable...

... springs (mechanical) damping nonlinear differential equations Historically the analysis community has acknowledged the role of joints in structural dynamics ambivalently. We ascribe the nonlinearities of our structures to the presence of joints, but we go ahead and use linear models. Though...

...-parity nonlinear oscillators. A quadratic–cubic nonlinear oscillator is used to verify and illustrate the usefulness and effectiveness of the proposed method. 17 07 2006 04 10 2006 nonlinear dynamical systems nonlinear differential equations oscillators perturbation theory...

... enhance our understanding of neural processing, we hope that it will serve as a fitting tribute to his work. neural nets variational techniques bifurcation nonlinear differential equations oscillations 21 11 2005 03 06 2006 2006 American Society...

... linearisation techniques nonlinear differential equations differential algebraic equations state-space methods The state of a multibody system at the position level is represented herein by an array q = [ q 1 , … , q p ] T of generalized coordinates. The velocity...