Reducing round-off errors in rigid body dynamics

Journal of Computational Physics

Volumn 227, Issue 15, 2008, Pages 7083-7088

  Vilmart, Gilles ^a,b  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b UNIVERSITY OF GENEVA   (Switzerland)

Author keywords

Compensated summation; Discrete Moser Veselov algorithm; Jacobi elliptic functions; Long time integration; Probabilistic error propagation; Quaternion; Rigid body integrator

Indexed keywords

ERRORS; RIGID STRUCTURES;

COMPENSATED SUMMATION; DISCRETE MOSER-VESELOV ALGORITHM; ERROR PROPAGATION; JACOBI ELLIPTIC FUNCTION; LONG TIME INTEGRATIONS; PROBABILISTIC ERROR PROPAGATION; PROBABILISTICS; QUATERNION; RIGID BODY; RIGID BODY INTEGRATOR;

EQUATIONS OF MOTION;

EID: 45449102829     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.04.013     Document Type: Article

References (14)

1. Brouwer D. On the accumulation of errors in numerical integration. Astronom. J. 46 (1937) 149-153
2. Celledoni E., Fassò F., Säfström N., and Zanna A. The exact computation of the free rigid body motion and its use in splitting methods. SIAM J. Sci. Comp. (2007)
3. Celledoni E., and Säfström N. Efficient time-symmetric simulation of torqued rigid bodies using Jacobi elliptic functions. J. Phys. A 39 (2006) 5463-5478
4. Fassò F. Comparison of splitting algorithm for the rigid body. J. Comput. Phys. 189 (2003) 527-538
5. Hairer E., Lubich C., and Wanner G. Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations. Springer Series in Computational Mathematics 31. second ed. (2006), Springer-Verlag, Berlin
6. Hairer E., McLachlan R.I., and Razakarivony A. Achieving Brouwer's law with implicit Runge-Kutta methods. BIT (2008)
7. Hairer E., and Vilmart G. Preprocessed discrete Moser-Veselov algorithm for the full dynamics of the rigid body. J. Phys. A 39 (2006) 13225-13235
8. Henrici P. Discrete Variable Methods in Ordinary Differential Equations (1962), John Wiley & Sons Inc., New York
9. Higham N.J. The accuracy of floating point summation. SIAM J. Sci. Comput. 14 (1993) 783-799
10. C.G.J. Jacobi, Sur la rotation d'un corps, Journal für die reine und angewandte Matematik (Journal de Crelle) 39 293-350, publ. 1850 (lu dans la séance du 30 juillet 1849 à l'académie des sciences de Paris).
11. Kahan W. Further remarks on reducing truncation errors. Comm. ACM 8 (1965) 40
12. Møller O. Quasi double-precision in floating point addition. BIT 5 (1965) 251-255
13. van Zon R., and Schofield J. Numerical implementation of the exact dynamics of free rigid bodies. J. Comput. Phys. 225 1 (2007) 145-164
14. van Zon R., and Schofield J. Symplectic algorithms for simulations of rigid body systems using the exact solution of free motion. Phys. Rev. E 75 (2007) 056701