When conventional integrators like Runge-Kutta-type algorithms are used,numerical errors can make an orbit deviate from a hypersurface determined by many constraints,which leads to unreliable numerical solutions.Scali...When conventional integrators like Runge-Kutta-type algorithms are used,numerical errors can make an orbit deviate from a hypersurface determined by many constraints,which leads to unreliable numerical solutions.Scaling correction methods are a powerful tool to avoid this.We focus on their applications,and also develop a family of new velocity multiple scaling correction methods where scale factors only act on the related components of the integrated momenta.They can preserve exactly some first integrals of motion in discrete or continuous dynamical systems,so that rapid growth of roundoff or truncation errors is suppressed significantly.展开更多
This paper relates to the post-Newtonian Hamiltonian dynamics of spinning compact binaries, consisting of the Newtonian Kepler problem and the leading, next-to-leading and next-to-next-to-leading order spin-orbit coup...This paper relates to the post-Newtonian Hamiltonian dynamics of spinning compact binaries, consisting of the Newtonian Kepler problem and the leading, next-to-leading and next-to-next-to-leading order spin-orbit couplings as linear functions of spins and momenta. When this Hamiltonian form is transformed to a Lagrangian form, besides the terms corresponding to the same order terms in the Hamiltonian, several additional terms, third post-Newtonian(3 PN),4 PN, 5 PN, 6 PN and 7 PN order spin-spin coupling terms, yield in the Lagrangian. That means that the Hamiltonian is nonequivalent to the Lagrangian at the same PN order but is exactly equivalent to the full Lagrangian without any truncations. The full Lagrangian without the spin-spin couplings truncated is integrable and regular. Whereas it is non-integrable and becomes possibly chaotic when any one of the spin-spin terms is dropped. These results are also supported numerically.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 10873007,11173012,11178002 and 11178014.
文摘When conventional integrators like Runge-Kutta-type algorithms are used,numerical errors can make an orbit deviate from a hypersurface determined by many constraints,which leads to unreliable numerical solutions.Scaling correction methods are a powerful tool to avoid this.We focus on their applications,and also develop a family of new velocity multiple scaling correction methods where scale factors only act on the related components of the integrated momenta.They can preserve exactly some first integrals of motion in discrete or continuous dynamical systems,so that rapid growth of roundoff or truncation errors is suppressed significantly.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11533004,11663005the Natural Science Foundation of Jiangxi Province under Grant Nos.20153BCB22001 and 20171BAB211005
文摘This paper relates to the post-Newtonian Hamiltonian dynamics of spinning compact binaries, consisting of the Newtonian Kepler problem and the leading, next-to-leading and next-to-next-to-leading order spin-orbit couplings as linear functions of spins and momenta. When this Hamiltonian form is transformed to a Lagrangian form, besides the terms corresponding to the same order terms in the Hamiltonian, several additional terms, third post-Newtonian(3 PN),4 PN, 5 PN, 6 PN and 7 PN order spin-spin coupling terms, yield in the Lagrangian. That means that the Hamiltonian is nonequivalent to the Lagrangian at the same PN order but is exactly equivalent to the full Lagrangian without any truncations. The full Lagrangian without the spin-spin couplings truncated is integrable and regular. Whereas it is non-integrable and becomes possibly chaotic when any one of the spin-spin terms is dropped. These results are also supported numerically.
