The accuracy of floating point summation
SIAM Journal on Scientific Computing
Pracniques: further remarks on reducing truncation errors
Communications of the ACM
Comparison of splitting algorithms for the rigid body
Journal of Computational Physics
Numerical implementation of the exact dynamics of free rigid bodies
Journal of Computational Physics
The Exact Computation of the Free Rigid Body Motion and Its Use in Splitting Methods
SIAM Journal on Scientific Computing
Energy stability and fracture for frame rate rigid body simulations
Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Algorithm 903: FRB--Fortran routines for the exact computation of free rigid body motions
ACM Transactions on Mathematical Software (TOMS)
Original article: Error growth in the numerical integration of periodic orbits
Mathematics and Computers in Simulation
Reducing rounding errors and achieving Brouwer's law with Taylor Series Method
Applied Numerical Mathematics
| Hi-index | 31.45 |
In several recent publications, numerical integrators based on Jacobi elliptic functions are proposed for solving the equations of motion of the rigid body. Although this approach yields theoretically the exact solution, a standard implementation shows an unexpected linear propagation of round-off errors. We explain how deterministic error contribution can be avoided, so that round-off behaves like a random walk.