共查询到20条相似文献，搜索用时 31 毫秒
1.
A recurrent method of solving the formal integrals of symplectic integrators is given. The special examples show that there are no long-term variations in all integrals of the Hamiltonian system in addition to the energy one when symplectic integrators are used in the numerical studies of the system. As an application of the formal integrals, the relation between them and the linear stability of symplectic integrators is discussed. 相似文献
2.
Xinhao Liao 《Celestial Mechanics and Dynamical Astronomy》1996,66(3):243-253
In this paper, following the idea of constructing the mixed symplectic integrator (MSI) for a separable Hamiltonian system, we give a low order mixed symplectic integrator for an inseparable, but nearly integrable, Hamiltonian system, Although the difference schemes of the integrators are implicit, they not only have a small truncation error but, due to near integrability, also a faster convergence rate of iterative solution than ordinary implicit integrators, Moreover, these second order integrators are time-reversible. 相似文献
3.
Haruo Yoshida 《Celestial Mechanics and Dynamical Astronomy》1993,56(1-2):27-43
In this paper various aspect of symplectic integrators are reviewed. Symplectic integrators are numerical integration methods for Hamiltonian systems which are designed to conserve the symplectic structure exactly as the original flow. There are explicit symplectic schemes for systems of the formH=T(p)+V(q), and implicit schemes for general Hamiltonian systems. As a general property, symplectic integrators conserve the energy quite well and therefore an artificial damping (excitation) caused by the accumulation of the local truncation error cannot occur. Symplectic integrators have been applied to the Kepler problem, the motion of minor bodies in the solar system and the long-term evolution of outer planets. 相似文献
4.
Massimiliano Guzzo 《Celestial Mechanics and Dynamical Astronomy》2001,80(1):63-80
I have improved the precision of the leap–frog symplectic integrators for perturbed Kepler problems at small eccentricities, without significant loss of CPU time. The integration scheme proposed is competitive, in some situations, with the so-called mixed variable integrators. 相似文献
5.
We review the implementation of individual particle time-stepping for N-body dynamics. We present a class of integrators derived from second order Hamiltonian splitting. In contrast to the usual implementation of individual time-stepping, these integrators are momentum conserving and show excellent energy conservation in conjunction with a symmetrized time step criterion. We use an explicit but approximate formula for the time symmetrization that is compatible with the use of individual time steps. No iterative scheme is necessary. We implement these ideas in the HUAYNO1 code and present tests of the integrators and show that the presented integration schemes shows good energy conservation, with little or no systematic drift, while conserving momentum and angular momentum to machine precision for long term integrations. 相似文献
6.
This paper deals mainly with the application of the mixed leapfrog symplectic integrators with adaptive timestep to a conservative post-Newtonian Hamiltonian formulation with canonical spins for spinning compact binaries. The adaptive timestep depends on the two body separation r and the magnitude of the spins. Various numerical tests including a chaotic high-eccentricity orbit show that the fixed step symplectic integrators lost drastically the good long term behaviour in the test cases with large eccentricity, the adaptive timestep integrator is always superior to the constant step in the integral precision. 相似文献
7.
Orbit propagation algorithms for satellite relative motion relying on Runge–Kutta integrators are non-symplectic—a situation that leads to incorrect global behavior and degraded accuracy. Thus, attempts have been made to apply symplectic methods to integrate satellite relative motion. However, so far all these symplectic propagation schemes have not taken into account the effect of atmospheric drag. In this paper, drag-generalized symplectic and variational algorithms for satellite relative orbit propagation are developed in different reference frames, and numerical simulations with and without the effect of atmospheric drag are presented. It is also shown that high-order versions of the newly-developed variational and symplectic propagators are more accurate and are significantly faster than Runge–Kutta-based integrators, even in the presence of atmospheric drag. 相似文献
8.
Solar System Research - The paper investigates the efficiency of the new collocation integrator Lobbie, presented in (Avdyushev, 2020), in comparison with other integrators widely used in practice,... 相似文献
9.
10.
Ariadna Farrés Jacques Laskar Sergio Blanes Fernando Casas Joseba Makazaga Ander Murua 《Celestial Mechanics and Dynamical Astronomy》2013,116(2):141-174
Using a Newtonian model of the Solar System with all 8 planets, we perform extensive tests on various symplectic integrators of high orders, searching for the best splitting scheme for long term studies in the Solar System. These comparisons are made in Jacobi and heliocentric coordinates and the implementation of the algorithms is fully detailed for practical use. We conclude that high order integrators should be privileged, with a preference for the new $(10,6,4)$ method of Blanes et al. (2013). 相似文献
11.
12.
13.
We review what kinds of numerical integrators are used by astronomers in the field of dynamical astronomy and to what problems they are applied. This review is based on the questionaires distributed mainly to the members of IAU Commission 7 (Celestial Mechanics). Because of the restriction to the Commission 7 members, the answers are mainly from astronomers in the solar system dynamics and problems mentioned in the answers are also related to celestial bodies in the solar system. Other than above, two questions, how to check the precision or accuracy of numerically integrated results and how to treat a close approach, are also surveyed. The problem of the suitable choice of a numerical integrator from various numerical integrators is out of the scope of this review, and it depends strongly on the dynamical nature of a particular dynamical system and the required accuracy. 相似文献
14.
We describe a numerical algorithm based on Godunov methods for integrating the equations of compressible magnetohydrodynamics (MHD) in multidimensions. It combines a simple, dimensionally-unsplit integration method with the constrained transport (CT) discretization of the induction equation to enforce the divergence-free constraint. We present the results of a series of fully three-dimensional tests which indicate the method is second-order accurate for smooth solutions in all MHD wave families, and captures shocks, contact and rotational discontinuities well. However, it is also more diffusive than other more complex unsplit integrators combined with CT. Thus, the primary advantage of the method is its simplicity. It does not require a characteristic tracing step to construct interface values for the Riemann solver, it is straightforward to extend with additional physics, and it is suitable for use with nested and adaptive meshes. The method is implemented as one of two dimensionally unsplit MHD integrators in the Athena code, which is freely available for download from the web. 相似文献
15.
We describe a parallel hybrid symplectic integrator for planetary system integration that runs on a graphics processing unit (GPU). The integrator identifies close approaches between particles and switches from symplectic to Hermite algorithms for particles that require higher resolution integrations. The integrator is approximately as accurate as other hybrid symplectic integrators but is GPU accelerated. 相似文献
16.
适用于人造卫星轨道数值积分的线性多步法的研究 总被引：4，自引：0，他引：4
总结了多年来构造适合卫星轨道计算的线性多步积分方法的研究进展;介绍了在构造积分公式的过程中选取伪根的三条原则。结合具体算例,对推荐的适用于不同类型卫星轨道的五线性多积分公式的性能与对称文坛及科威尔方法作了详细地比对和评述。 相似文献
17.
Jean-Marc Petit 《Celestial Mechanics and Dynamical Astronomy》1998,70(1):1-21
We investigate the numerical implementation of a symplectic integrator combined with a rotation (as in the case of an elongated
rotating primary). We show that a straightforward implementation of the rotation as a matrix multiplication destroys the conservative
property of the global integrator, due to roundoff errors. According to Blank et al. (1997), there exists a KAM-like theorem
for twist maps, where the angle of rotation is a function of the radius. This theorem proves the existence of invariant tori
which confine the orbit and prevent shifts in radius. We replace the rotation by a twist map or a combination of shears that
display the same kind of behaviour and show that we are able not only to recover the conservative properties of the rotation,
but also make it more efficient in term of computing time. Next we test the shear combination together with symplectic integrator
of order 2, 4, and 6 on a Keplerian orbit. The resulting integrator is conservative down to the roundoff errors. No linear
drift of the energy remains, only a divergence as the square root of the number of iterations is to be seen, as in a random
walk. We finally test the three symplectic integrators on a real case problem of the orbit of a satellite around an elongated
irregular fast rotating primary. We compare these integrators to the well-known general purpose, self-adaptative Bulirsch–Stoer
integrator. The sixth order symplectic integrator is more accurate and faster than the Bulirsch–Stoer integrator. The second-
and fourth- order integrators are faster, but of interest only when extreme speed is mandatory.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
18.
徐继鸿 《中国科学院上海天文台年刊》2002,(1)
概述了制约线性多步积分公式轨道积分状态的多种因素 ;提出了综合评价线性多步积分公式积分性能的两项新指标。建议在对数值计算有较高精度要求的科研项目中 ,应将构造并选择适合研究项目的线性多步积分公式以及高效的积分方式列为课题前期工作的重要部分 相似文献
19.
An operator associated with third-order potential derivatives and a force gradient operator corresponding to second-order potential derivatives are used together to design a number of new fourth-order explicit symplectic integrators for the natural splitting of a Hamiltonian into both the kinetic energy with a quadratic form of momenta and the potential energy as a function of position coordinates.Numerical simulations show that some new optimal symplectic algorithms are much better than their non-optimal c... 相似文献
20.
RKNF方法和大偏心率轨道数值积分 总被引：1，自引：0，他引：1
本文比较在建立中等和大偏心率轨道的精密数值历表时几种数值方法的计算效率,特别推荐国内轨道工作中尚未见使用的直接积分２ 阶微分方程的ＲＫＮＦ 方法。数值实算表明,在方程右函数显含速度和中等或大偏心率轨道情况下,嵌套的７ 阶方法ＲＫＮＦ７８ 是一个普适性好、效率高、程序设计简单的方法。 相似文献