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Original Articles

A State-Space-Based Implicit Integration Algorithm for Differential-Algebraic Equations of Multibody DynamicsFootnote*

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Pages 311-334 | Received 01 Oct 1996, Published online: 03 Apr 2007

REFERENCES

  • T. J. Hughes The Finite Element Method , Prentice-Hall , Englewood Cliffs , New Jersey , 1987 .
  • L. R. Petzold Differential/algebraic equations are not ODE's , SlAM Journal of Scientific and Statistical Computing 3 ( 3 ) 367 – 384 ( 1982 ).
  • K.E. Brenan , S. L. Campbell , and L. R. Petzold The Numerical Solution of Initial Value Problems in Ordinary differential-algebraic Equations , pnNorth Holland Publishing Co.|pn, New York , 1989 .
  • J. Baumgarte Stabilization of constraints and integrals of motion in dynamical system , Comp. Meth. in Appl. Mech. and Eng. 1 1 – 16 ( 1972 ).
  • G. P. Ostermeyer Baumgarte stabilization for differential-algebraic equations , NATO Advanced Research Workshop in Real Time Simulation , E. J. Haug and R. Deyo, eds. , Springer-Verlag , Berlin , 1990 .
  • U. M. Ascher , H. Chin , L. R. Petzold , and S. Reich Stabilization of constrained mechanical systems with DAEs and invariant manifolds , Mech. Struct. & Mach. 23 ( 2 ) 135 – 157 ( 1995 ).
  • E. Eich , C. Fuhrer , B.J. Leimkuhler , and S. Reich Stabilization and Projection Methods for Multibody Dynamics , Tech. Report , Helsinki University of Technology , Finland , 1990 .
  • C.W. Gear , G. K. Gupta , and B.J. Leimkuhler Automatic integration of the Euler-Lagrange equations with constraints , J. Comp. Appl. Math. 12–13 pp77–90|pp ( 1985 ).
  • C. Fuhrer and B.J. Leimkuhler Numerical solution of differential-algebraic equations for constrained mechanical motion , Numerische Mathematik , 59 55 – 69 ( 1991 ).
  • F. Potra and W. C. Rheinboldt On the numerical integration for Euler-Lagrange equations via tangent space parametrization , Mech. Struct. Mach. 19 1 ( 1991 ).
  • R. A. Wehage , and E. J. Haug Generalized coordinate partitioning for dimension reduction in analysis of constrained dynamic systems , J. Mech. Design 134 247 – 255 ( 1982 ).
  • N.K. Mani , E. J. Haug , and K. E. Atkinson Application of singular value decomposition for analysis of mechanical system dynamics , J. of Mechanisms, Transmissions, and Automation in Design 107 82 – 87 ( 1985 ).
  • C. G. Liang and G. M. Lance 1987 , A differentiable null space method for constrained dynamic analysis , J. of Mechanisms. Transmissions, and Automation in Design 109 405 – 411 .
  • E. J. Haug , and J. Yen Implicit numerical integration of constrained equation of motion via generalized coordinate partitioning , J. Mechanical Design 114 296 – 304 ( 1992 ).
  • J. Yen and L. R. Petzold On the Numerical Solution of Constrained Multibody Dynamic System , AHPCRC TRT 94-038 , University of Minnesota , 1995 .
  • P. Fisette and B. Vaneghem Numerical integration of multibody dynamic equations using the coordinate partitioning method in an implicit Newmark scheme , Comput. Methods Appl. Mech. Engrg. 135 85 – 105 ( 1996 ).
  • K. E. Atkinson An Introduction to Numerical Analysis, 2d Edition , John Wiley & Sons , New York , 1989 .
  • E. J. Haug Computer Aided Kinematics and Dynamics of Mechanical Systems Volume 1 Basic Methods , Allyn-Bacon , Boston , 1989 .
  • L. J. Corwin and R. H. Szczarba Multivariable Calculus , Marcel Dekker , New York , 1982 .
  • W. Schiehlen Multibody Handbook , Springer-Verlag , New York , 1990 .
  • E. Hairer , and G. Wanner Solving Ordinary Differential Equations II Stiff and Differential-Algebraic Problems , Springer-Verlag , Berlin , 1991 .
  • *Communicated by E. J. Haug

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