...). Next, the period-doubling instability regions for a particular delay differential equation related to the damped Meissner’s equation and the fold instabilities for a model of delayed position feedback control are analytically obtained. Finally, we extend the method to a single degree-of-freedom milling...

... is described by a fractional differential equation of order less than 1, and the fractional derivative is defined in terms of Riemann–Liouville. The performance index includes the terminal cost function in addition to the integral cost function. A general transversility condition in addition to the optimal...

... -trigonometric functions further infer fractional differential equations, which, based on power law parametric functions, are used to develop a fractional growth equation modeling evolution from conception to maturity. An important aspect of this work is that it demonstrates a method of determination...

...–Stokes equations are projected onto these POD modes to reduce the dynamical system to a set of ordinary-differential equations (ODEs). This dynamical system exhibits a limit cycle with negative linear damping and positive nonlinear damping. The reduced-order model is then modified by placing a pair...

.... The fractional Hamiltonian on the extended phase space is analyzed and the corresponding generalized Poisson’s brackets are constructed. 08 06 2009 20 08 2009 12 08 2010 12 08 2010 calculus differential equations Fokker-Planck equation The fractional calculus is as old...

... rotations together with small elastic deformations. The two-stage and three-stage algorithms are modified to integrate the finite element based, second order differential equations of multibody dynamics directly. A new simplified Newton iteration is implemented for the two-stage algorithm to reduce its...

...Martin Arnold The interacting components of complex technical systems are often described by coupled systems of differential equations. In dynamical simulation, these coupled differential equations have to be solved numerically. Cosimulation techniques, multirate methods, and other approaches...

... deformation theory based finite element method (FEM). The governing equations are integrated using Newmark’s time marching coupled with shooting technique and arc-length continuation. Shooting method is used to solve the second-order differential equations of motion directly without converting them...

... advantageous than the integer ones. differential equations eigenvalues and eigenfunctions hysteresis integral equations optimisation three-term control Mainardi , F. , 1996 , “ The Fundamental Solutions for the Fractional Diffusion-Wave Equation ,” Appl. Math. Lett. 0893-9659 , 9...

... and depth of cut. Dynamic systems such as milling are modeled by delay-differential equations with time-periodic coefficients. A new approximation technique for studying the stability properties of such systems is presented. The approach is based on the properties of Chebyshev polynomials and a collocation...

... synchronized action of the sign-changeable antitorque is proposed and applied. All investigations are carried out within the fields of qualitative theory of differential equations and nonlinear dynamics. The mentioned boundary conditions are as follows. 1 Simply supported arc slice, 14 w n , j...

... theory is demonstrated. Several specific differential equations are presented, and their initialization responses are found for a variety of initializations. Both the time-domain and Laplace-domain solutions are obtained and compared. The complementary incomplete gamma function is shown to be essential...

...Carl F. Lorenzo; Tom T. Hartley It has been known that the initialization of fractional operators requires time-varying functions, a complicating factor. This paper simplifies the process of initialization of fractional differential equations by deriving Laplace transforms for the initialized...

...Liming Dai; Guoqing Wang The present research intends to investigate the characteristics of the periodicity ratio and its implementation in analyzing the nonlinear behavior of dynamic systems governed by second-order differential equations. Numerical analyses on the nonlinear dynamic systems...

... delay-differential equations, there exists an appropriate method for determining the stability boundary curve in the domain of technological parameters. The stability boundary is implicitly defined as a level set of a function on the parameter domain, which makes the evaluation computationally expensive...

... with the classical one leading to a system of ordinary differential equations. The approach using reference conditions is motivated either from the need of keeping the error introduced when linearizing the elastic forces as small as possible (Buckens frame) or from minimizing the relative kinetic energy contained...

... to be computed before the stability can be investigated. This periodic solution is computed using a finite difference method for delay-differential equations. Especially for low immersion cuts, the stability lobes diagram (SLD) using the updated model shows significant differences compared to the SLD using...

... initial ones due to different angles of impact. The differential equation-based computational model is shown to be realistic and efficient in simulating impact sequence and laid a foundation for detailed finite element analysis of the interior impact response of an electronic device. The equation...

...Pankaj Kumar; Om P. Agrawal This paper presents a numerical scheme for the solutions of Fractional Differential Equations (FDEs) of order α , 1 < α < 2 which have been expressed in terms of Caputo Fractional Derivative (FD). In this scheme, the properties of the Caputo derivative are used...

... of numerical computation. Our investigation of the thermal mechanical response of laminate considers thermal stress and strain in the nonlinear elastic deformation of the laminate. We have found that the equation of motion can be reduced to a decoupled nonlinear differential equation in a multimode...