An overview of MEXX: Numerical Software for the Integration of Multibody Systems. MEXX (short for MEXanical systems eXtrapolation integrator) is a Fortran code for time integration of constrained mechanical systems, which was developed at the University of Innsbruck and the Konrad-Zuse-Center Berlin. It is suited for direct integration of the equations of motion in descriptor form, and has the following features: Time stepping by a half-explicit extrapolation method, allowing for the accurate and robust computation of position, velocity, acceleration, and constraint forces. Only position and velocity constraint functions are evaluated, acceleration constraints need not be formulated. Both position and velocity constraints remain satisfied throughout the integration interval. Uses well-structured linear algebra, enabling the use of O(n) recursive elimination, among other full and sparse linear algebra options. Time-continuous solution representation (e.g., for graphics). Root-finding options (e.g., for impact and Coulomb friction problems). MEXX encourages the use of large, sparse descriptor formulations, but can also efficiently handle near-statespace kinematic formulations of multibody systems. A detailed description of MEXX and the underlying concepts is given in [5]. In the present short note we provide a brief overview.

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  1. Sætran, Nicolai; Zanna, Antonella: Chains of rigid bodies and their numerical simulation by local frame methods (2019)
  2. Arnold, Martin: DAE aspects of multibody system dynamics (2017)
  3. Burger, Michael; Gerdts, Matthias: A survey on numerical methods for the simulation of initial value problems with sDAEs (2017)
  4. Simeon, Bernd: On the history of differential-algebraic equations. A retrospective with personal side trips (2017)
  5. Carpinelli, Mariano; Gubitosa, Marco; Mundo, Domenico; Desmet, Wim: Automated independent coordinates’ switching for the solution of stiff DAEs with the linearly implicit Euler method (2016)
  6. Andersson, C., Führer, C., Åkesson, J.: Assimulo: A unified framework for ODE solvers (2015) not zbMATH
  7. Andersson, Christian; Führer, Claus; Åkesson, Johan: Assimulo: a unified framework for ODE solvers (2015)
  8. Blajer, Wojciech: Methods for constraint violation suppression in the numerical simulation of constrained multibody systems - A comparative study (2011)
  9. Masarati, Pierangelo: Adding kinematic constraints to purely differential dynamics (2011)
  10. Hamann, Peter; Mehrmann, Volker: Numerical solution of hybrid systems of differential-algebraic equations (2008)
  11. Terze, Zdravko; Naudet, Joris: Geometric properties of projective constraint violation stabilization method for generally constrained multibody systems on manifolds (2008)
  12. Arnold, Martin; Burgermeister, Bernhard; Eichberger, Alexander: Linearly implicit time integration methods in real-time applications: DAEs and stiff ODEs (2007)
  13. Arnold, M.; Fuchs, A.; Führer, C.: Efficient corrector iteration for DAE time integration in multibody dynamics (2006)
  14. Gear, C. W.: Towards explicit methods for differential algebraic equations (2006)
  15. Simeon, Bernd: On Lagrange multipliers in flexible multibody dynamics (2006)
  16. Anderson, K. S.; Duan, S.: A hybrid parallelizable low-order algorithm for dynamics of multi-rigid-body systems. I: Chain systems. (1999)
  17. Arnold, M.: The stabilization of linear multistep methods for constrained mechanical systems (1998)
  18. Engstler, Christian; Kaps, Peter: A comparison of one-step methods for multibody system dynamics in descriptor and state space form (1997)
  19. Simeon, B.: On the numerical solution of a wheel suspension benchmark problem (1996)
  20. Rheinboldt, W. C.; Simeon, B.: Performance analysis of some methods for solving Euler-Lagrange equations (1995)