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A recursive multibody formalism for systems with small mass and inertia terms

M. Arnold
2013 Mechanical Sciences  
</strong> Complex multibody system models that contain bodies with small mass or nearly singular inertia tensor may suffer from high frequency solution components that deteriorate the solver efficiency  ...  In the present paper, a recursive multibody formalism is developed to evaluate the equations of motion for a tree structured <i>N</i> body system with <i>O(N)</i> complexity even if isolated bodies have  ...  Singular perturbations in multibody system models After a short introduction to singularly perturbed ODEs we consider in the present section singular perturbations in multibody system models that are caused  ... 
doi:10.5194/ms-4-221-2013 fatcat:ny5ct5m7enbirbcdsq4ddajmcu

Isogeometric shell discretizations for flexible multibody dynamics

Anmol Goyal, Michael R. Dörfel, Bernd Simeon, Anh-Vu Vuong
2013 Multibody system dynamics  
Bernd Simeon for providing me with an opportunity to work under his able supervision.  ...  I would always be indebted to him for his invaluable guidance and belief in my abilities throughout the duration of my research.  ...  This is a singularly perturbed system with perturbation parameter .  ... 
doi:10.1007/s11044-013-9343-1 fatcat:joqckq2a3jayfhvqcitdwowhqe

Exponential Integrators for Large Systems of Differential Equations

Marlis Hochbruck, Christian Lubich, Hubert Selhofer
1998 SIAM Journal on Scientific Computing  
For large problems, these can be approximated by Krylov subspace methods, which typically converge faster than those for the solution of the linear systems arising in standard sti integrators.  ...  We derive methods up to order 4 which are exact for linear constant-coe cient equations. The implementation of the methods is discussed.  ...  In Section 4 we extend the methods to di erential-algebraic systems. We derive order conditions up to order 3 for such problems and for singularly perturbed systems.  ... 
doi:10.1137/s1064827595295337 fatcat:fd6z3xfdezeadbobwhnunfq5kq

Book Review: Lectures on finite precision computations

Hans J. Stetter, Charles Van Loan, Michael Holst, Frank Stenger, Chi-Wang Shu, R. Mattheij, Stephen J. Wright, Thomas F. Coleman, Lars B. Wahlbin
1997 Mathematics of Computation  
Interestingly some DAE appear naturally as a limiting case of a singularly perturbed ODE, i.e. the reduced equation. This then explains the strong relationship to numerical methods for stiff ODE (cf.  ...  This book could be used in a course on parallel numerical methods for model elliptic equations in two dimensions.  ... 
doi:10.1090/s0025-5718-97-00910-1 fatcat:kiiohmhwnrh5rkjl672eqoqnre

Fourier's Method of Linear Programming and Its Dual

H. P. Williams
1986 The American mathematical monthly  
[See also 70F25] 70E20 Perturbation methods for rigid body dynamics 70E40 Integrable cases of motion 70E45 Higher-dimensional generalizations 70E50 Stability problems 70E55 Dynamics of multibody  ...  theory 93A10 General systems 93A13 Hierarchical systems 93A14 Decentralized systems 93A15 Large scale systems 93A30 Mathematical modeling (models of systems, model-matching, etc.) 93A99 None  ...  classification number from Section 01) 83-04 Explicit machine computation and programs (not the theory of computation or programming) 83-05 Experimental work conferences, collections, Computational methods  ... 
doi:10.2307/2322281 fatcat:yvhgyh2epbcwdoqdhuaopkcrue

Port-Hamiltonian descriptor systems [article]

Christopher Beattie and Volker Mehrmann and Hongguo Xu and Hans Zwart
2017 arXiv   pre-print
It is shown that this structure is invariant under equivalence transformations, and that it is adequate also for the modeling of high-index descriptor systems.  ...  The modeling framework of port-Hamiltonian systems is systematically extended to constrained dynamical systems (descriptor systems, differential-algebraic equations).  ...  The second author has been supported by Deutsche Forschungsgemeinschaft for Research support via Project A02 in CRC 1029 TurbIn and by Einstein Foundation Berlin within the Einstein Center ECMath.  ... 
arXiv:1705.09081v2 fatcat:bia7sm5hrffk3b2jfrig7sqtp4

Numerical Stabilization of the Melt Front for Laser Beam Cutting [chapter]

Torsten Adolph, Willi Schönauer, Markus Niessen, Wolfgang Schulz
2010 Numerical Mathematics and Advanced Applications 2009  
The resulting linear systems are solved alternatively by the Multigrid method and Krylov subspace methods. We treat two types of boundary conditions: Dirichlet and natural boundary condition.  ...  The model is based on Navier-Stokes equations for viscous incompressible flow and convection-diffusion equation describing pollution transport.  ...  time-stepping methods for finite element approximations of singularly perturbed parabolic problems or hyperbolic problems.  ... 
doi:10.1007/978-3-642-11795-4_6 fatcat:nx4nvuxaxfbcdjknopny53ck5e

Page 531 of Mathematical Reviews Vol. 28, Issue Index [page]

Mathematical Reviews  
J.; et al., (96m:65066) Dimitrova, Angela Slavova Constructive method for solving nonlinear singularly perturbed systems. 96a:34118 Ding, Zuo Hua On a class of implicit differential inclusions.  ...  (English summary) 96¢e:34096 Arnold, Martin A perturbation analysis for the dynamical simulation of mechanical multibody systems. (English summary) 96i:65007 Ascher, Uri M. (with Petzold, Linda R.)  ... 

On data-dependence of exponential stability and stability radii for linear time-varying differential-algebraic systems

Chuan-Jen Chyan, Nguyen Huu Du, Vu Hoang Linh
2008 Journal of Differential Equations  
Then, it is investigated that how the Bohl exponent and the stability radii with respect to dynamic perturbations for a differentialalgebraic system depend on the system data.  ...  Linh, Stability radii for linear timevarying differential-algebraic equations with respect to dynamic perturbations, J. Differential Equations 230 (2006) 579-599].  ...  Acknowledgment The authors are greatly indebted to an anonymous referee for useful comments leading to the improvement of the paper.  ... 
doi:10.1016/j.jde.2008.07.016 fatcat:me5hw5j2gjg5va4c33au2fetwm

Modelling and Discretization of Circuit Problems [chapter]

Michael Günther, Uwe Feldmann, Jan ter Maten
2005 Handbook of Numerical Analysis  
However, this will yield singularly perturbed problems, which will not at all be preferable to DAE models in numerical respect.  ...  Chapter I DAE-Systems -the modelling aspect In computational engineering the network modelling approach forms the basis for computeraided analysis of time-dependent processes in multibody dynamics, process  ... 
doi:10.1016/s1570-8659(04)13006-8 fatcat:h3l2jw323rbnbdz7y5wec3zitm

Computation of Singular and Singularity Induced Bifurcation Points of Differential-Algebraic Power System Model

S. Ayasun, C.O. Nwankpa, H.G. Kwatny
2004 IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications  
The proposed method is implemented into voltage stability toolbox and simulations results are presented for a 5-bus and IEEE 118-bus systems.  ...  In this paper, we present an efficient algorithm to compute singular points and singularity-induced bifurcation points of differential-algebraic equations for a multimachine power-system model.  ...  [27] have proposed a singularly perturbed differential equation (SPDE) as the power-system model and their simulation results indicate that rapid decline in bus voltage magnitudes may occur if trajectories  ... 
doi:10.1109/tcsi.2004.832741 fatcat:pilkanjmhnhf3mbkyh2tedpqbu

Page 1307 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
Minimax methods for designing dynamical systems. (Russian.  ...  ., 91¢:93037 70Q Control of mechanical systems 70Q0S Orlov, G. M. A method for the analytic construction of a control on the basis of optimal damping. (Russian) 91g:90213 Osipov, S.  ... 

Grafische Programmentwicklung mit GRAPES® [chapter]

J. Wagner
1986 Informatik-Anwendungen — Trends und Perspektiven  
The problem of an efficient solution of the singularly perturbed elliptic subproblems and the problem of error estimation for them can be uniquely solved within the framework of preconditioning.  ...  Walter: A Finite Element Method Adaptive in Space and Time for Nonlinear Reaction Diffusion Systems.  ... 
doi:10.1007/978-3-642-71388-0_31 dblp:conf/gi/Wagner86 fatcat:snijjy7vb5azzmquu4ivbgxe7m

Page 2006 of Mathematical Reviews Vol. 32, Issue Index [page]

Mathematical Reviews  
Modern analytical methods applied to mechanical engineering systems.  ...  Analytical methods in dynamical simulation of flexible multibody systems. (English summary) 2000h:70003 Pian, Theodore H. H. see He, Guojing et al. Pivovarchik, Vyacheslav N.  ... 

Page 1433 of Mathematical Reviews Vol. , Issue Author Index [page]

Mathematical Reviews  
The asymptotic method of differential inequalities for singularly perturbed integrodifferential equations. (Russian. Russian summary) Differ.  ...  Development of the asymptotic method of differential inequalities for step-type solutions in singularly perturbed integrodifferential equations. (Russian. Russian summary) Zh. Vychisl. Mat. Mat.  ... 
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