Numerical Methods for Constrained Equations of Motion in Mechanical System Dynamics

REFERENCES

• E. J. Haug , Computer Aided Kinematics and Dynamics of Mechanical Systems Vol. I . Basic Methods , Allyn and Bacon , Boston , 1989 .
   Google Scholar
• J. Wittenburg , Dynamics of Systems of Rigid Bodies , B. G. Teubner , Stuttgart , 1977 .
   Google Scholar
• K. Brenan , S. Campbell , and L. Petzold , Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations , North-Holland , New York , 1989 .
   Google Scholar
• C. Führer and B. Leimkuhler , Numerical solution of differential-algebraic equations for constrained mechanical motion, submitted to Numerische Mathemalik in September 1989 .
   Google Scholar
• C. W. Gear , Differential-algebraic equation index transformations , SIAM J. Sci. Stat. Comput . 9 34 – 37 ( 1988 ).
   Google Scholar
• L. R. Petzold , Differential/algebraic equations are not ODEs , SIAM J. Sci. Stat. Comput . 3 376 – 384 ( 1982 ).
   Google Scholar
• C. W. Gear , Numerical Initial Value Problems in Ordinary Differential Equations , Prentice-Hall , Englewood Cliffs , New Jersey , 1971 .
   Google Scholar
• E. J. Haug and J. Yen , “ Generalized Coordinate Partitioning Methods for Numerical Integration of Differential-Algebraic Equations of Dynamics ,” Technical Report 39 , Center for Simulation and Design Optimization of Mechanical Systems, University of Iowa , Iowa City , Iowa , May 1989 .
   Google Scholar
• L. R. Petzold , A. description of DASSL A differential/algebraic system solver , IMACS Trans. on Sci. Comput. , Vol. I , North Holland , New York , 1982 , pp. 65 – 68 .
   Google Scholar
• L. R. Petzold and P. Lotstedt , Numerical solution of nonlinear differential equations with algebraic constraints Part II. Practical implementations , SIAM J. Sci. Stat. Comput. 7 720 – 733 ( 1986 ).
   Google Scholar
• C. W. Gear , B. Leimkuhler , and G. K. Gupta , Automatic integration of Euler-Lagrange equations with constraints , J. Comput. Appl. Math. 12/13 77 – 90 ( 1985 ).
   Google Scholar
• C. Führer and B. Leimkuhler , “ A New Class of Generalized Inverses for the Solution of Discretized Euler-Lagrange Equations ,” NATO Advanced Research Workshop on Real-Time Integration Methods for Mechanical System Simulation , Snowbird , Utah , U.S.A. , August 7 – 11 , 1989 .
   Google Scholar
• DADS User's Manual , Rev. 4.0, Computer Aided Design Software, Inc. , Oakdale , Iowa , 1987 .
   Google Scholar
• W. C. Rheinboldt , Numerical Analysis of Parametrized Nonlinear Equations , Wiley , New York , 1986 .
   Google Scholar
• W. C. Rheinboldt , “ On the Existence and Computation of Solutions of Nonlinear Semi-Implicit Differential Algebraic Equations ,” University of Pittsburgh, Institute of Computer Mathematics and Applications , Pittsburgh , Pennsylvania , Technical Report ICMA - 89 – 139 , August 1989 ; submitted to SIAM J. Numer. Anal.
   Google Scholar
• F. A. Potra and J. Yen , “ Implicit Numerical Integration for Euler-Lagrange Equations Via Tangent Space Parametrization ,” Technical Report 56, Center for Simulation and Design Optimization of Mechanical Systems , University of Iowa , Iowa City , Iowa , May 1989 .
   Google Scholar
• K. E. Atkinson , Introduction to Numerical Analysis , 2d ed. , Wiley , New York , 1989 .
   Google Scholar
• L. F. Shampine and M. K. Gordon , Computer Solution ofODEs the Initial Value Problem . W. H. Freeman & Co. , San Francisco , 1975 .
   Google Scholar
• J. Yen , “ Numerical Methods for Constrained Equations of Motion in Mechanical System Dynamics ,” Ph.D. thesis. Applied Mathematical Sciences , University of Iowa , Iowa City , Iowa , May 1990 .
   Google Scholar
• W. M. Boothby , An Introduction to Differential Manifolds and Riemannian Geometry , 2d ed. , Academic Press , New York , 1986 .
   Google Scholar
• J. E. Dennis and R. Schnobel , Numerical Methods for Unconstrained Minimization and Nonlinear Equations , Prentice Hall , Englewood Cliffs , New Jersey , 1983 .
   Google Scholar
• L. F. Shampine and H. A. Watts , “ DEPAC-Design of a User Oriented Package of ODE Solvers ,” SAND 79 – 2374 , Sandia National Laboratory , Albuquerque , New Mexico , 1980 .
   Google Scholar
• J. M. Ortega and W. C. Rheinboldt , Iterative Solution of Nonlinear Equations in Several Variables , Academic Press , New York , 1970 .
   Google Scholar
• A. K. Cline , C. B. Moler , G. W. Steward , and J. H. Wilkinson , An estimate for the condition number of a matrix , SIAM J. Numer. Anal. 16 368 – 375 ( 1979 ).
   Web of Science ®Google Scholar
• G. H. Golub and C. F. VanLoan , Matrix Computations , Johns Hopkins University Press , Baltimore , Maryland , 1983 .
   Google Scholar
• J. J. Dongarra , C. B. Moler , J. R. Bunch , and C. W. Steward , Linpack User's Guide , SIAM , Philadelphia , 1979 .
   Google Scholar