... the representation’s scope of applicability. Future work will investigate generating stochastic terrain surfaces with these vectors. 08 07 2010 27 07 2011 04 08 2011 12 01 2012 12 01 2012 Galerkin method Hilbert spaces matrix algebra measurement systems polynomials vehicle...

... of the squeeze-film damping. 26 02 2010 08 06 2011 05 12 2011 05 12 2011 beams (structures) clamps damping finite difference methods finite element analysis Galerkin method impact (mechanical) micromechanical devices MEMS squeeze film damping nonlinear mechanics...

... implemented on physical systems without observing uncertain parameters. 18 09 2008 29 08 2010 29 10 2010 29 10 2010 chaos control system synthesis Galerkin method linear quadratic control polynomials probability state-space methods uncertain systems polynomial chaos...

... through base excitation and two piezoelectric elements are attached to the beam for vibration control purposes. The distributed-parameter model for the beam-element system is discretized by using Galerkin’s method, and time histories of the system’s response describe the controller’s attenuation...

... and Control Division January 3, 2003; final revision, September 22, 2003. Associate Editor: C. D. Rahn. 03 January 2003 22 September 2003 05 08 2004 closed loop systems deformation distributed parameter systems compliance control Galerkin method fasteners transfer functions...

... estimation Galerkin method numerical analysis 02 03 2003 27 03 2004 Equation 11 by direct numerical simulation: b 2 = π ∕ 4 , F = 3 π ∕ 2 , ω = 2 π Equation 11 by numerical simulation of ODEs: same parameter as in Fig. 7 , N = 5...

... differential equations by means of the Karhunen-Loe`ve Galerkin procedure which is a type of Galerkin method employing the empirical eigenfunctions of the Karhunen-Loe`ve decomposition. Employing the Kalman filter constructed by using the reduced order model, the thermal convection induced by a spatially...

... control problem of the heat conduction equation. The Karhunen–Loe`ve Galerkin procedure, which is a Galerkin method employing the empirical eigenfunctions of the Karhunen–Loe`ve decomposition as trial functions, limits the function space considered to the smallest linear subspace that is sufficient...