... fluid oscillations Lyapunov methods noise pipe flow stochastic processes 2011 American Society of Mechanical Engineers ...

... = 0 , and ν 0 = 2 ω 1 ( K = 12 ) 25 01 2008 16 09 2008 22 04 2009 damping eigenvalues and eigenfunctions Lyapunov methods method of moments noise partial differential equations resonance stability stochastic processes...

... is negative, system 1 is asymptotically stable with probability 1. diffusion linear differential equations Lyapunov methods Monte Carlo methods numerical analysis stability stochastic systems 14 03 2006 02 10 2008 03 03 2009 Step 3 . Solve the discretized system...

... equations Lyapunov methods noise stability vibrations viscoelasticity Mathematically, random excitations can be described as stochastic processes. With the theory of stochastic processes, analytical models of different noises can be established. Gaussian white noise process ξ ( t...

... the line OI. 03 12 2004 19 12 2005 kinematics mechanical contact state-space methods nonlinear control systems Lyapunov methods stability force feedback biomechanics legged locomotion Part of the directly and easily measurable quantities are ground reaction forces...

... after final publication in the paper itself in the ASME JOURNAL OF APPLIED MECHANICS . 03 January 2004 17 September 2004 15 03 2005 Monte Carlo methods Lyapunov methods stochastic systems white noise stability Stochastic differential equations are encountered...

... a hyperspherical transformation and under the ergodicity assumption they investigated the Lyapunov exponents with the aid of ensemble averaging rather than time averaging. nonlinear dynamical systems mechanical stability stochastic processes asymptotic stability Lyapunov methods exponential...

... mechanical stability eigenvalues and eigenfunctions Lyapunov methods This paper is concerned with stochastic stability of two-degree-of-freedom (dof) systems in the presence of internal resonances . In linear multi-degree-of-freedom systems, resonances occur due to commensurability...

... by Tsinias 9 . eigenvalues and eigenfunctions feedback differential equations dynamic programming stochastic programming Lyapunov methods optimal control asymptotic stability 12 July 2000 15 January 2002 23 01 2003 Contributed by the Applied Mechanics Division...

... Lyapunov methods viscoelasticity vibrations stochastic processes eigenvalues and eigenfunctions mechanical stability random noise On the other hand, the stability of the p th moment of the trivial solution of system ( 1 ), E [ ‖ x t ‖ p ] , is determined by the moment...

... of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS . 15 May 2000 26 Feb 2001 mechanical stability noise stochastic processes Lyapunov methods oscillations classical mechanics In the study of stability of solutions of random dynamical systems, the exponential growth...

... Nov 1999 08 Nov 2000 bifurcation Lyapunov methods elasticity mechanical stability vibrations stochastic processes damping Investigations of the dynamic stability of elastic systems, such as the transverse vibration of columns and flat plates under randomly fluctuating axial...