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Full-Text Articles in Physical Sciences and Mathematics
Comparative Study Of Louville And Symplectic Integrators, Daniel I. Okunbor
Comparative Study Of Louville And Symplectic Integrators, Daniel I. Okunbor
Computer Science Technical Reports
In this paper, we construct an integrator that conserves volume in phase space. We compare the results obtained using this method and a symplectic integrator. The results of our experiments do not reveal any superiority of the symplectic over strictly volume-preserving integrators. We also investigate the effect of numerically conserving energy in a numerical process by rescaling velocities to keep energy constant at every step. Our results for Henon-Heiles problem show that keeping energy constant in this way destroys ergodicity and forces the solution onto a periodic orbit.
Time-Discretization Of Hamiltonian Dynamical Systems, Yosi Shibberu
Time-Discretization Of Hamiltonian Dynamical Systems, Yosi Shibberu
Mathematical Sciences Technical Reports (MSTR)
Difference equations for Hamiltonian systems are derived from a discrete variational principle. The difference equations completely determine piecewise-linear, continuous trajectories which exactly conserve the Hamiltonian function at the midpoints of each linear segment. A generating function exists for transformations between the vertices of the trajectories. Existence and uniqueness results are present as well as simulation results for a simple pendulum and an inverse square law system.