zbMATH — the first resource for mathematics

Numerical solution of differential-algebraic equations for constrained mechanical motion. (English) Zbl 0701.70003
Summary: The two most popular formulations of the equations of constrained mechanical motion, the descriptor and state-space forms, each have severe practical limitations. In this paper, we discuss and relate some proposed reformulations of the equations which have improved numerical properties.

70A05 Axiomatics, foundations
70Sxx Classical field theories
65L05 Numerical methods for initial value problems involving ordinary differential equations
Full Text: DOI EuDML
[1] Alishenas, T., Dahlquist, G.: Personal communication. KTH Stockholm 1989
[2] Arnold, V.I.: Mathematical methods of classical mechanics. Berlin Heidelberg New York: Springer 1978 · Zbl 0386.70001
[3] Brenan, K.B., Campbell, S.L., Petzold, L.R.: Numerical solution of initial value problems in ordinary differential-algebraic equations. New York Amsterdam London: North Holland 1989 · Zbl 0699.65057
[4] Campbell, S.L., Meyer, C.D.: Generalized inverses of linear transformations. Montreal: Pitman 1979 · Zbl 0417.15002
[5] Campbell, S.L., Leimkuhler, B.: Differentiation of constraints in differential-algebraic equations. Mech. Struct. Machines (to appear)
[6] Lawson, C.L., Hanson, R.J.: Solving Least squares problems. Englewood Cliffs: Prentice-Hall 1974 · Zbl 0860.65028
[7] F?hrer, C.: Differential-algebraische Gleichungssysteme in mechanischen Mehrk?rpersystemen. TU M?nchen, Thesis, Mathematisches Institut, TU M?nchen, TUM-M 8807, August 1988
[8] F?hrer, C., Leimkuhler, B.J.: Formulation and numerical solution of the equations of constrained mechanical motion. Technical Report DFVLR-FB 89-08, Deutsche Forschungs-und Versuchsanstalt f?r Luft- und Raumfahrt (DFVLR), K?ln 1989
[9] F?hrer, C., Schwertassek, R.: Generation and solution of multibody system equations. Int. J. Nonl. Mechanics25, 127-141 (1990) · Zbl 0711.70015
[10] Gear, C.W.: Maintaining solution invariants in the numerical solution of ode. SIAM J. Sci. Stat. Comput.7, 734-743 (1986) · Zbl 0614.65076
[11] Gear, C.W., Gupta, G.K., Leimkuhler, B.J.: Automatic integration of the Euler-Lagrange equations with constraints. J. Comput. Appl. Math.12 & 13, 77-90 (1985) · Zbl 0576.65072
[12] Gear, C.W., Petzold, L.R.: ODE Methods for the solution of differential/algebraic systems. Technical Report UIUCDCS-R-82-1103, University of Illinois, Urbana 1982 · Zbl 0557.65053
[13] Griepentrog, E., M?rz, R.: Differential-algebraic equations and their numerical treatment. Teubner-Texte zur Mathematik No. 88, Leipzig: Teubner 1986 · Zbl 0629.65080
[14] Hairer, E., Lubich, C., Roche, M.: The numerical solution of differential-algebraic equations by Runge-Kutta methods. Lecture Notes in Mathematics, 1409. Berlin Heidelberg New York: Springer 1989 · Zbl 0683.65050
[15] Leimkuhler, B.J.: Some notes on perturbations of differential-algebraic equations. Technical Report, Institute of Mathematics, Helsinki University of Technology (1989)
[16] Leimkuhler, B.J., Petzold, L.R., Gear, C.W.: Approximation methods for the consistent initialization of differential-algebraic equations. SIAM J. Numer Anal.28 (Feb. 1991) (to appear) · Zbl 0725.65076
[17] Lubich, C.: h2 Extrapolation methods for differential-algebraic equations of index-2. Technical Report, Universit?t Innnsbruck, Institut f?r Mathematik und Geometrie, Innnsbruck (1988) · Zbl 0676.65078
[18] Nikravesh, P.E.: Some methods for dynamical analysis of constrained mechanical systems: a survey. In: Haug, E.J. (ed.) Computer aided analysis and optimization of mechanical system dynamics, pp. 223-259. Berlin Heidelberg New York: Springer 1984
[19] Ortega, J.M., Rheinboldt, W.C.: Iterative solutions of nonlinear equations in several variables. New York: Academic Press 1970 · Zbl 0241.65046
[20] Ostermeyer, G.: Die Stabilisierung von Bindungen und ersten Integralen als Regelungsproblem und ihre Konsequenzen. ZAMM Z. Angew. Math. Mech.65, 185-187 (1985) · Zbl 0574.70013
[21] Ostermann, A.: A half-explicit extrapolation method for differential-algebraic systems of index 3. Technical Report, Universit? de Gen?ve, Dept. de math?matiques 1989 · Zbl 0704.65051
[22] Park, C.T., Haug, E.J.: Numerical methods for mixed differential-algebraic equations in kinematics and dynamics. PhD thesis, College of Engineering, University of Iowa, Iowa city 1985
[23] Petzold, L.R.: A description of DASSL: a differential/algebraic system solver. In: Stepleman, R.S. (ed.) IMACS Trans. Sci. Comput. Vol. 1, p. 65. Amsterdam: North Holland 1983
[24] Reich, S.: Beitrag zur Theorie der Algebrodifferentialgleichungen. Thesis, Fakult?t f?r Elektrotechnik/Elektronik, Technische Universit?t Dresden (1989)
[25] Rheinboldt, W.C.: Differential?algebraic systems as differential equations on manifolds. Math. Comput.43, 473-482 (1984) · Zbl 0581.65058
[26] Roberson, R.E., Schwertassek, R.: Dynamics of multibody systems. Berlin Heidelberg New York: Springer 1988 · Zbl 0654.70001
[27] Rulka, W.: SIMPACK, A computer program for simulatio of large-motion multibody systems. In: Schiehlen, W. (ed.) Multibody handbook, pp. 265-284. Berlin Heidelberg New York: Springer 1990
[28] Schiehlen, W.: Multibody handbook. Berlin Heidelberg New York: Springer 1990 · Zbl 0703.70002
[29] Shampine, L.F.: Conservation laws and the numerical solution of ODEs. Technical Report 84-1241, Sandia National Laboratories, Livermore 1984 · Zbl 0947.65086
[30] Starner, J.W.: A numerical algorithm for the solution of implicit algebraic-differential systems of equations. PhD thesis, University of New Mexico (1976)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.