.... 30 07 2017 30 10 2017 Analytical solution systems Continuation Methods Nonlinear dynamical systems Nonlinear oscillations Nonlinear phenomena Stability Stochastic systems Symbolic solution systems Vibration Writing Eq. (4) in state space form (5) { d...

.... Editor: Hiroshi Yabuno. 03 08 2017 05 10 2017 Analytical solution systems Nonlinear oscillations Symbolic solution systems Vibration In 1968, Prigogine and Lefever [ 1 ] proposed the chemical reaction scheme, which is called a Brusselator. Such an oscillator...

... equations. The knowledge symmetries are important, sometimes just as important as the conserved quantity itself. Excellent textbooks for symmetry methods include [ 4 , 5 ]. Analytical solution systems Nonlinear dynamical systems Symbolic solution systems 08 09 2017 21 05 2018...

... 2018 21 05 2018 Analytical solution systems Computational dynamics Nonlinear dynamical systems Nonlinear phenomena Symbolic solution systems Bio-mechanical systems Biological systems The Newel–Whitehead–Segel equation (NWSE), one of the significant concepts of pattern...

... Stability Symbolic solution systems Stability of nonlinear systems 30 11 2017 24 04 2018 Contributed by the Design Engineering Division of ASME for publication in the J OURNAL OF C OMPUTATIONAL AND N ONLINEAR D YNAMICS . Manuscript received November 30, 2017; final manuscript...

... received September 6, 2017; final manuscript received March 19, 2018; published online April 12, 2018. Assoc. Editor: Massimo Ruzzene. 06 09 2017 19 03 2018 Analytical solution systems Experimental dynamics Symbolic solution systems In 2000, Landa and McClintock [ 1...

... Analytical solution systems Nonlinear dynamical systems Nonlinear oscillations Perturbation Symbolic solution systems Vibration Asymptotic models The linear normal mode is an established concept in the structural dynamics theory, which has been widely used in various industrial applications...

... into the parametric instability have been gained based on different models [ 2 – 29 ]. This work focuses on the accurate and complete comparison in terms of instabilities. Analytical solution systems Control Stability Symbolic solution systems Stability of nonlinear systems 01 08 2017 05 11...

... Analytical solution systems Symbolic solution systems Symmetry analysis has many applications in the field of science and engineering. Lie's method is one of the global and efficient method for investigating analytical solutions and symmetry properties of nonlinear partial differential equations...

... Numerical Symbolic solution systems Integration methods Linear ordinary differential equations with time-periodic coefficients have a wide range of applications in various fields of science and engineering. Some of their applications include structures subjected to periodic loads [ 1 ], helicopter...

... Control Non-smooth dynamics Symbolic solution systems Stability of nonlinear systems Discontinuous dynamical systems extensively exist in engineering, such as mechanical engineering and engineering control. One tried to use the existing methods in continuous dynamical systems for solving...

... dynamics Nonlinear dynamical systems Nonlinear oscillations Nonlinear phenomena Perturbation Symbolic solution systems Vibration Dynamics of NEMS Dynamics of MEMS Asymptotic models 08 11 2016 16 05 2017 Contributed by the Design Engineering Division of ASME for publication...

...; final manuscript received June 1, 2017; published online July 12, 2017. Assoc. Editor: Hiroshi Yabuno. 13 12 2016 01 06 2017 Analytical solution systems Control Experimental dynamics Nonlinear dynamical systems Symbolic solution systems Stability of nonlinear systems...

... Stepan. 15 06 2015 10 11 2015 Analytical solution systems Symbolic solution systems Derivative on fractals (as a special case of time scales) has been proposed in Ref. [ 1 ] by (1) D α f ( t ) : = lim t ′ → t f ( t ) − f ( t...

... integration of Eq. (31) over I z  7:  update I according to Eq. (26) Algorithms Analytical solution systems Computational mechanics Impact Contact Friction modeling Numerical Symbolic solution systems Integration methods A collision between two rigid bodies is often...

... Algorithms Analytical solution systems Fractional calculus Integration methods Symbolic solution systems In the past few decades, fractional calculus has attained considerable popularity and importance as generalizations of integer-order evolution equations and used to model problems in neurons...

... online December 5, 2016. Assoc. Editor: Jozsef Kovecses. 09 11 2015 14 06 2016 Algorithms Analytical solution systems Computational kinematics Nonlinear dynamical systems Numerical Symbolic solution systems Dynamics Integration methods Constrained dynamical systems...

... methods Symbolic solution systems In this study, a new numerical scheme based on quasilinearization and Chebyshev wavelet is proposed for the coupled sine-Gordon equation of the form (1.1) { u t t − u x x = − δ 2   sin ( u − w ) + f ( x , t...

... with nonlinear functions described as (1) f ( x ¨ , x ˙ , x , t ) = 0 Analytical solution systems Nonlinear dynamical systems Symbolic solution systems 31 08 2015 03 07 2016 Contributed by the Design Engineering Division of ASME for publication...

... of all the solutions simultaneously beyond the degeneracy as long as their number is finite. Analytical solution systems Impact Contact modeling Symbolic solution systems is a plane rotation matrix. Without loss of generality, we choose the common frame g to be the body-fixed...