MEXX - Numerical Software for the Integration of Constrained Mechanical Multibody Systems

MEXX (short for MEXanical systems eXtrapolation integrator) is a Fortran code for time integration of constrained mechanical systems. MEXX is suited for direct integration of the equations of motion in descriptor form. It is based on extrapolation of a time stepping method that is explicit in the differential equations and linearly implicit in the nonlinear constraints. It only requires the solution of well–structured systems of linear equations which can be solved with a computational work growing linearly with the number of bodies, in the case of multibody systems with few closed kinematic loops. Position and velocity constraints are enforced throughout the integration interval, whereas acceleration constraints need not be formulated. MEXX has options for time–continuous solution representation (useful for graphics) and for the location of events such as impacts. The present article describes MEXX and its underlying concepts. * Universität Würzburg ** Universität Innsbruck This work was supported in part by a Konrad Zuse Fellowship, and by the Austrian Science Foundation project P8443–PHY.

[1]  C. Paige,et al.  An error analysis of a method for solving matrix equations , 1973 .

[2]  J. Wittenburg,et al.  Dynamics of systems of rigid bodies , 1977 .

[3]  Iain S. Duff,et al.  MA28 --- A set of Fortran subroutines for sparse unsymmetric linear equations , 1980 .

[4]  H. Idelberger,et al.  Dynamische Vorgänge bei Lastumlagerung in Abspannketten von Freileitungen , 1980 .

[5]  E. Haug,et al.  Generalized Coordinate Partitioning for Dimension Reduction in Analysis of Constrained Dynamic Systems , 1982 .

[6]  P. Deuflhard.  Order and stepsize control in extrapolation methods , 1983 .

[7]  Peter Deuflhard,et al.  Recent progress in extrapolation methods for ordinary differential equations , 1985 .

[8]  Martin Otter,et al.  A very efficient algorithm for the simulation of robots and similar multibody systems without invers , 1986 .

[9]  Per Lötstedt,et al.  Numerical solution of nonlinear differential equations with algebraic contraints II: practical implications , 1986 .

[10]  E. Hairer,et al.  Solving Ordinary Differential Equations I , 1987 .

[11]  I. Duff,et al.  On Sparse Solvers in a Stiff Integrator of Extrapolation Type , 1987 .

[12]  E. Haug,et al.  A Recursive Formulation for Constrained Mechanical System Dynamics: Part II. Closed Loop Systems , 1987 .

[13]  E. Hairer,et al.  Extrapolation at stiff differential equations , 1988 .

[14]  Ronald L. Huston,et al.  Dynamics of Multibody Systems , 1988 .

[15]  Ernst Hairer,et al.  The numerical solution of differential-algebraic systems by Runge-Kutta methods , 1989 .

[16]  R. Schwertassek,et al.  Recursive Generation of Multibody System Equations in Terms of Graph Theoretic Concepts , 1989 .

[17]  E. J. Haug,et al.  Computer aided kinematics and dynamics of mechanical systems. Vol. 1: basic methods , 1989 .

[18]  E. Hairer,et al.  Dense output for extrapolation methods , 1990 .

[19]  Å. Björck.  Least squares methods , 1990 .

[20]  P. Rentrop,et al.  Differential-algebraic Equations in Vehicle System Dynamics , 1991 .

[21]  H. Brauchli,et al.  Dynamical equations in natural coordinates , 1991 .

[22]  Christian Lubich,et al.  Extrapolation integrators for constrained multibody systems , 1991, IMPACT Comput. Sci. Eng..

[23]  I. Duff,et al.  The factorization of sparse symmetric indefinite matrices , 1991 .

[24]  J. Müller.  Dynamische Vorgänge bei Brüchen in Isolatoren-Doppelketten von Freileitungen : Analyse der Lastumlagerung , 1991 .

[25]  F. Potra.  Implementation of linear multistep methods for solving constrained equations of motion , 1993 .

[26]  Ernst Hairer,et al.  Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .

[27]  P. Rentrop,et al.  A nonlinear truck model and its treatment as a multibody system , 1994 .

[28]  Linda R. Petzold,et al.  Numerical solution of initial-value problems in differential-algebraic equations , 1996, Classics in applied mathematics.