A simplified implicit Newmark integration scheme for finite rotations

Computers and Mathematics with Applications

Volumn 53, Issue 2, 2007, Pages 219-231

  Rubin, M B ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Finite rotations; Implicit integration; Newmark; Rotation vector

Indexed keywords

ANGULAR VELOCITY; APPROXIMATION THEORY; CONTINUUM MECHANICS; EULER EQUATIONS; NEWTON-RAPHSON METHOD;

FINITE ROTATIONS; IMPLICIT INTEGRATION; IMPLICIT NEWMARK SCHEMES; ROTATION TENSOR; ROTATION VECTOR;

INTEGRATION;

EID: 34247505513     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2006.02.021     Document Type: Article

References (15)

1. Antman S.S. The Theory of Rods. Handbuch der Physik vol. VIa/2 (1972), Springer-Verlag, Berlin
2. Simo J.C. A finite strain beam formulation. The three-dimensional dynamic problem. Part I. Computer Methods in Applied Mechanics and Engineering 49 (1985) 55-70
3. Simo J.C., and Vu-Quoc L. On the dynamics in space of rods undergoing large motions - A geometrically exact approach. Computer Methods in Applied Mechanics and Engineering 66 (1988) 125-161
4. Makinen J. Critical study of Newmark-scheme on manifold of finite rotations. Computer Methods in Applied Mechanics and Engineering 191 (2001) 817-828
5. Shuster M.D. A survey of attitude representations. Journal of Astronautical Sciences 41 (1993) 439-517
6. Bauchau O.A., and Trainelli L. The vectorial parameterization of rotation. Nonlinear Dynamics 32 (2003) 71-92
7. Hughes P.C. Spacecraft Attitude Dynamics (1986), Wiley, New York
8. Argyris J. An excursion into large rotations. Computer Methods in Applied Mechanics and Engineering 32 (1982) 85-155
9. Argyris J., and Poterasu V.F. Large rotations revisited application of Lie algebra. Computer Methods in Applied Mechanics and Engineering 103 (1993) 11-42
10. Stuelpnagel J. On the parameterization of the three-dimensional rotation group. SIAM Review 6 (1964) 422-430
11. Pfister F. Bernoulli numbers and rotational kinematics. ASME Journal of Applied Mechanics 65 (1998) 758-763
12. Ibrahimbegovic A. On the choice of finite rotation parameters. Computer Methods in Applied Mechanics and Engineering 149 (1997) 49-71
13. Beatty M.F. Vector analysis of finite rigid rotations. ASME Journal of Applied Mechanics 47 (1977) 501-502
14. Pietraszkiewicz W. Bernoulli numbers and rotational kinematics. ASME Journal of Applied Mechanics 66 (1999) 576
15. Dahlquist G., and Bjorck A. Numerical Methods (1974), Prentice-Hall, New Jersey