Differentiation of constraints in differential-algebraic equations*

Mechanics of Structures and Machines

Volumn 19, Issue 1, 1991, Pages 19-39

  Campbell, Stephen L ^a   Leimkuhler, B ^b  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b AALTO UNIVERSITY   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0013196171     PISSN: 08905452     EISSN: None     Source Type: Journal    
DOI: 10.1080/08905459108905136     Document Type: Article

References (12)

1. K. E. Brenan, S. L. Campbell, and L. R. Petzold, The Numerical Solution of Initial Value Problems in Ordinary Differential-Algebraic Equations, North Holland, New York, 1989.
2. C. W. Gear, Differential-algebraic equation index transformations, SIAM J. Sci. Stat. Comput. 7: 39–47 (1988).
3. S. L. Campbell, A computational method for general higher index singular systems of differential equations, IMACS Transactions on Scientific Computing, Paris, 1988, Vol. 1. 2, 1989, pp. 555-560.
4. V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer-Verlag, New York, 1978.
5. T. Mrziglod, “Zur Theorie und numerischen Realisierung von Lösungmethoden bei Dif-ferentialgleichungen mit angekoppelten algebraischen Gleichungcn,” Diplomarbeit, Mathematischen Institut, Universität zu Köln, Cologne, Germany, 1987.
6. C. F. Fürher and B. Leimkuhler, “Formulation and Numerical Solution of the Equations of Constrained Mechanical Motion.” Technical Report DFVLR-FB 89–08, Deutsche For-schungs-und Veruchsanstalt für Luftund Raumfahrt, Oberpfaffenhofen, Germany, 1989.
7. L. R. Petzold, Observations on an adaptive moving grid method for one-dimensional systems of partial differential equations, Appl. Numer. Math. 3: 347–360 (1987).
8. L. M. Silverman, Inversion of multivariate systems, IEEE Trans. Autom. Control, AC-14: 270–276 (1969).
9. J. Baumgarte, Stabilization of constraint and integrals of motion in dynamical systems, Comput. Methods Appl. Mech. Eng. 1: 1–16 (1972).
10. L. F. Shampine, “Conservation Laws and the Numerical Solution of ODEs,” Technical Report 84–1241, Sandia National Laboratories, Livermore, California, 1984.
11. C. W. Gear, Maintaining solution invariants in the numerical solution of ODEs, SIAM J. Sci. Stat. Comput. 7(3): 734-743 (1986).
12. C. F. Fiihrer, “Differential-algebraische Gleichungssysteme in mechanischen Mehrkörpersystemen,” Ph.D. thesis, Mathematisehes Institut, Technische Universität Munchen, Munich, 1988.