Numerical recipes in Fortran 90 (2nd ed.): the art of parallel scientific computing
Numerical recipes in Fortran 90 (2nd ed.): the art of parallel scientific computing
Algorithm 577: Algorithms for Incomplete Elliptic Integrals [S21]
ACM Transactions on Mathematical Software (TOMS)
A Changing-Chart Symplectic Algorithm for Rigid Bodies and Other Hamiltonian Systems on Manifolds
SIAM Journal on Scientific Computing
Practical symplectic partitioned Runge--Kutta and Runge--Kutta--Nyström methods
Journal of Computational and Applied Mathematics
Comparison of splitting algorithms for the rigid body
Journal of Computational Physics
The Discrete Moser–Veselov Algorithm for the Free Rigid Body, Revisited
Foundations of Computational Mathematics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Numerical implementation of the exact dynamics of free rigid bodies
Journal of Computational Physics
Short Note: Reducing round-off errors in rigid body dynamics
Journal of Computational Physics
The Exact Computation of the Free Rigid Body Motion and Its Use in Splitting Methods
SIAM Journal on Scientific Computing
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We present two algorithms and their corresponding Fortran routines for the exact computation of free rigid body motions. The methods use the same description of the angular momentum part m by Jacobi elliptic functions, and suitably chosen frames for the attitude matrix/quaternion Q/q, respectively. The frame transformation requires the computation of elliptic integrals of the third kind. Implementation and usage of the routines are described, and some examples of drivers are included. Accuracy and performance are also tested to provide reliable numerical results.