A variational splitting integrator for quantum molecular dynamics
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Comparison of splitting algorithms for the rigid body
Journal of Computational Physics
Preserving poisson structure and orthogonality in numerical integration of differential equations
Computers & Mathematics with Applications
Algorithm 903: FRB--Fortran routines for the exact computation of free rigid body motions
ACM Transactions on Mathematical Software (TOMS)
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We revive the elementary idea of constructing symplectic integrators for Hamiltonian flows on manifolds by covering the manifold with the charts of an atlas, implementing the algorithm in each chart (thus using coordinates) and switching among the charts whenever a coordinate singularity is approached. We show that this program can be implemented successfully by using a splitting algorithm if the Hamiltonian is the sum H1+H2 of two (or more) integrable Hamiltonians. Profiting from integrability, we compute exactly the flows of H1 and H2 in each chart and thus compute the splitting algorithm on the manifold by means of its representative in any chart. This produces a symplectic algorithm on the manifold which possesses an interpolating Hamiltonian, and hence it has excellent properties of conservation of energy. We exemplify the method for a point constrained to the sphere and for a symmetric rigid body under the influence of positional potential forces.