Abstract
A differential-geometric approach for the numerical solution of mixed differential-algebraic systems of equations is presented and a general local parametrization for such systems is constructed. Multistep ODE solvers are then applied for obtaining locally a numerical approximation to the solution of the differential-algebraic system. The class of local parametrizations considered in the paper contains as particular cases, the ‘tangent space’ parametrization and the local parametrization induced by the ‘generalized coordinate partitioning’. Applications for the numerical solution of the Euler-Lagrange equations are discussed in detail and computational results for a four-bar linkage mechanism are given.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
K.Brennan, S.Campbell, L.Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations,North-Hollond,New-York,1989.
DADS User’s Manual, Rev. 4. 0, Computer Aided Design Software, Inc., Oakdale, Iowa, 1987.
G.H.Golub, C.F.VanLoan, Matrix Computations, Johns Hopkins Univ. Press, Baltimore,MD 1983.
E. Griepentrog, R. Maerz, Differential-Algebraic Equations and Their Numerical Treatment, B.G.Teubner Verlag, Leipzig, 1986.
E.J.Haug,J.Yen, Implicit Numerical Integration of Constrained Equations of Motion via Generalized Coordinate Partitioning, Univ. of Iowa, Ctr. for Simulation and Design Optim. of Mech. Systems, Tech. Rep. R-39, Feb. 1989.
S.Lang, Introduction to Differentiable Manifolds, Wiley, New York, NY, 1962.
J.M. Ortega, W.C.Rheinboldt, Iterative Methods for Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
F.A.Potra, J.Yen, Implicit Numerical Integration for Euler-Lagrange Equations via Tangent Space Parametrization, Univ. of Iowa, Ctr. for Simulation and Design Optim. of Mech. Systems, Tech. Rep. R-56, June
S.Reich, Beitraege zur Theorie der Algebrodifferentialgleichungen, Ph.D. Dissertation (Electronics), Techn. Univ. Dresden, Spring 1988.
W. C. Rheinboldt, Differential-Algebraic Systems as Differential Equations on Manifolds, Math, of Comp. 43, 1984, 473 - 482.
W.C. Rheinboldt, Numerical Analysis of Parametrized Nonlinear Equations, John Wiley and Sons, New York, 1986.
W.C.Rheinboldt, On the Existence and Computation of Solutions of Nonlinear Semi-Implicit Algebraic Equations, University of Pittsburgh, Inst. f. Comp. Math, and Appl., Tech. Rep. ICMA-89-139, August 1989; SIAM J. Num. Anal., submitted.
M Spivak, A Comprehensive Introduction to Differential Geometry, Vol 1-5, Publish or Perish, Inc. Boston, MA 1970.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Potra, F.A., Rheinboldt, W.C. (1990). Differential-Geometric Techniques for Solving Differential Algebraic Equations. In: Haug, E.J., Deyo, R.C. (eds) Real-Time Integration Methods for Mechanical System Simulation. NATO ASI Series, vol 69. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76159-1_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-76159-1_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-76161-4
Online ISBN: 978-3-642-76159-1
eBook Packages: Springer Book Archive