共查询到20条相似文献，搜索用时 15 毫秒
1.
We construct an explicit reversible symplectic integrator for the planar 3-body problem with zero angular momentum. We start with a Hamiltonian of the planar 3-body problem that is globally regularised and fully symmetry reduced. This Hamiltonian is a sum of 10 polynomials each of which can be integrated exactly, and hence a symplectic integrator is constructed. The performance of the integrator is examined with three numerical examples: The figure eight, the Pythagorean orbit, and a periodic collision orbit. 相似文献
2.
Sławomir Breiter 《Celestial Mechanics and Dynamical Astronomy》1998,71(4):229-241
An explicit symplectic integrator is constructed for perturbed elliptic orbits of an arbitrary eccentricity. The perturbation
should be Hamiltonian, but it may depend on time explicitly. The main feature of the integrator is the use of KS variables
in the ten-dimensional extended phase space. As an example of its application the motion of an Earth satellite under the action
of the planet's oblateness and of lunar perturbations is studied. The results confirm the superiority of the method over a
classical Wisdom–Holman algorithm in both accuracy and computation time.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
3.
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
4.
We obtain thex - p
xPoincare phase plane for a two dimensional, resonant, galactic type Hamiltonian using conventional numerical integration,
a second order symplectic integrator and a map based on the averaged Hamiltonian. It is found that all three methods give
good results, for small values of the perturbation parameter, while the symplectic integrator does a better job than the mapping,
for large perturbations. The dynamical spectra are used to distinguish between regular and chaotic motion. 相似文献
5.
By Hamiltonian manipulation we demonstrate the existence of separable time‐transformed Hamiltonians in the extended phase‐space.
Due to separability explicit symplectic methods are available for the solution of the equations of motion. If the simple leapfrog
integrator is used, in case of two‐body motion, the method produces an exact Keplerian ellipse in which only the time‐coordinate
has an error. Numerical tests show that even the rectilinear N‐body problem is feasible using only the leapfrog integrator.
In practical terms the method cannot compete with regularized codes, but may provide new directions for studies of symplectic
N‐body integration.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
6.
当史瓦西黑洞周围存在渐近均匀的外部磁场时, 描述带电粒子在史瓦西黑洞附近运动的哈密顿系统会变为不可积系统. 类似于这样的相对论哈密顿系统不存在有显式分析解的2部分分离形式, 给显式辛算法的构建和应用带来困难. 近一年以来的系列工作提出将相对论哈密顿系统分解为具有显式分析解的2个以上分离部分形式, 成功解决了许多相对论时空构建显式辛算法的难题. 最近的工作回答了哈密顿系统显式可积分离数目对长期数值积分精度有何影响、哪种显式辛算法有最佳长期数值性能这两个问题, 指出哈密顿有最小可积分离数目即3部分分裂解形式并且应用于优化的4阶分段龙格库塔显式辛算法可取得最好精度. 由此选择上述数值积分方法并利用庞加莱截面、最大李雅普诺夫指数和快速李雅普诺夫指标研究在磁化史瓦西黑洞附近运动的带电粒子轨道动力学. 结果显示: 针对某特定的粒子能量和角动量, 较小的外部磁场很难形成混沌轨道; 较大的正磁场参数容易使轨道产生混沌, 并且随着磁场的增大, 轨道的混沌程度也随之加强; 粒子能量适当变大也可以加剧混沌程度, 但负磁场参数和粒子角动量变大都会减弱混沌. 相似文献
7.
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
8.
几类辛方法的数值稳定性研究 总被引：1，自引：0，他引：1
主要对一阶隐式Euler辛方法M1、二阶隐式Euler中点辛方法M2、一阶显辛Euler方法M3和二阶leapfrog显辛积分器M4共4种辛方法及一些组合算法进行了通常意义下的线性稳定性分析．针对线性哈密顿系统,理论上找到每个数值方法的稳定区,然后用数值方法检验其正确性．对于哈密顿函数为实对称二次型的情况,为了理论推导便利,特推荐采用相似变换将二次型的矩阵对角化来研究辛方法的线性稳定性．当哈密顿分解为一个主要部分和一个小摄动次要部分且二者皆可积时,无论是线性系统还是非线性系统,这种主次分解与哈密顿具有动势能分解相比,明显扩大了辛方法的稳定步长范围． 相似文献
9.
《Chinese Astronomy and Astrophysics》2005,29(1):92-103
The symplectic integrator has been regarded as one of the optimal tools for research on qualitative secular evolution of Hamiltonian systems in solar system dynamics. An integrable and separate Hamiltonian system H = H0 + Σi=1N εiHi (εi ≪ 1) forms a pseudo third order symplectic integrator, whose accuracy is approximately equal to that of the first order corrector of the Wisdom-Holman second order symplectic integrator or that of the Forest-Ruth fourth order symplectic integrator. In addition, the symplectic algorithm with force gradients is also suited to the treatment of the Hamiltonian system H = H0(q,p) + εH1(q), with accuracy better than that of the original symplectic integrator but not superior to that of the corresponding pseudo higher order symplectic integrator. 相似文献
10.
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
11.
Vacheslav Emel'yanenko 《Celestial Mechanics and Dynamical Astronomy》2002,84(4):331-341
A new symplectic algorithm is developed for cometary orbit integrations. The integrator can handle both high-eccentricity orbits and close encounters with planets. The method is based on time transformations for Hamiltonians separated into Keplerian and perturbation parts. The adaptive time-step of this algorithm depends on the distance from a centre and the magnitude of perturbations. The explicit leapfrog technique is simple and efficient. 相似文献
12.
The behaviour of ‘resonances’ in the spin-orbit coupling in celestial mechanics is investigated in a conservative setting.
We consider a Hamiltonian nearly-integrable model describing an approximation of the spin-orbit interaction. The continuous
system is reduced to a mapping by integrating the equations of motion through a symplectic algorithm. We study numerically
the stability of periodic orbits associated to the above mapping by looking at the eigenvalues of the matrix of the linearized
map over the full cycle of the periodic orbit. In particular, the value of the trace of the matrix is related to the stability
character of the periodic orbit. We denote by ε*
(p/q) the value of the perturbing parameter at which a given elliptic periodic orbit with frequency p/q becomes unstable. A plot of the critical function ε*
(p/q) versus the frequency at different orbital eccentricities shows significant peaks at the synchronous resonance (for low eccentricities)
and at the synchronous and 3:2 resonances (at higher eccentricities) in good agreement with astronomical observations.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
13.
We revisit a set of symplectic variables introduced by Andre Deprit (Celest Mech 30, 181–195, 1983), which allows for a complete symplectic reduction in rotation invariant Hamiltonian systems, generalizing to arbitrary dimension
Jacobi’s reduction of the nodes. In particular, we introduce an action-angle version of Deprit’s variables, connected to the
Delaunay variables, and give a new hierarchical proof of the symplectic character of Deprit’s variables. 相似文献
14.
关于近地小行星轨道演化的初步探索 总被引：2，自引：0，他引：2
本文采用改进的显式辛算法和嵌套的PKF7（8）积分器同时对86颗已命名（或编号）的近地小行星的轨道演化进行了数值研究，在103－104年的时间尺度上，给出了这些小行星轨道演化的状况以及它们与几颗大行星靠近的最小距离，特别是与地球接近的最小距离可小于0．01天文单位，甚至可能比月球还更靠近地球． 相似文献
15.
辛积分器中沿迹误差的一种补偿方法 总被引：2，自引：0，他引：2
辛积分器严格描述了一摄动Ｈａｍｉｌｔｏｎ系统的流，因而导致天体轨道的沿迹误差随时间呈线性增长趋势。本文利用这一特点，提出了一种对其沿迹误差进行估算的数值方法，从而达到了对数值结果进行沿迹误差补偿的目的，数值结果证实了此方法在较大积分步长和较长积分时间的数值计算中是有效的。 相似文献
16.
The Effect of C22 on Orbit Energy and Angular Momentum 总被引：1，自引：0，他引：1
D.J. Scheeres 《Celestial Mechanics and Dynamical Astronomy》1999,73(1-4):339-348
The effect of the C22 gravity field term on a particle is evaluated analytically over one orbit to find the change in orbit energy and angular
momentum as an explicit function of the orbital inclination, argument of pericenter, longitude of the ascending node, orbit
parameter and eccentricity. Changes in orbit energy and angular momentum are shown to be proportional to a family of integrals
which can be parameterized in terms of eccentricity and non-dimensional pericenter radius.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
17.
In addition to the detection of an asteroid moon or a binary asteroid, the knowledge of the satellite’s true orbit is of high importance to derive fundamental physical parameters of the binary system such as its mass and to shed light on its possible formation history and dynamical evolution (prograde/retrograde orbit, large/small eccentricity or inclination, etc.). A new methodology for preliminary orbit determination of binary asteroids – and visual binaries in general – is proposed. It is based on Thiele–Innes method combined with a ‘trial and error’ Monte-Carlo technique. This method provides the full set of solutions (bundle of orbits, with the 7 orbital elements) even for a reduced number of observations. The mass is a direct by-product of this orbit determination, from which one can next infer the bulk-density and porosity. In addition to the bundle of orbits, the method provides the marginal probability densities of the foreseen parameters. Such error analysis – since it avoids linear approximation – can be of importance for the prediction of the satellite’s position in the plane-of-sky during future stellar occultations or subsequent observations, but also for the analysis of the orbit’s secular evolution. After briefly describing the method, we present the algorithm and its application to some practical cases, with particular emphasis on asteroids binaries and applications on orbital evolution. 相似文献
18.
Ashraf Hamdy Mostafa K. Ahmed Mohamad Radwan Fawzy Ahmed Abd El-Salam 《Earth, Moon, and Planets》2003,93(4):261-273
The objective of the present work is to develope explicit analytical expressions for the small amplitude orbits of the infinitesimal
mass about the equilibrium points in the elliptic restricted three body problem. To handle this dynamical problem, the Hamiltonian
for the elliptic problem is formed with the true anomaly and then with the eccentric anomaly as independent variables. The
origin is then transformed to a fixed point and the Hamiltonian is developed up to O(4) in the eccentricity, e, (which plays the role of the small parameter of the problem) of the primaries. The integration of the model problem under
consideration is undertaken by means of a perturbation technique based on Lie series developments, which leads to the solution
of the canonical equations of motion. 相似文献
19.
辛算法在动力天文中的应用（Ⅲ） 总被引：3，自引：0，他引：3
文［１］和文［２］从哈密顿系统的整体结构保持一角度阐明了辛算法［３－６］的主要功能，本文将从定量的角度进一步表明辛算法的另一独特优点－可以控制天体运动沿迹误差的快速增长，并对可分离哈密顿系统的显式辛差分格式稍加改进，推广应用到一般动力系统，该系统含有小耗散项或小的不可分离项，计算结果表明，效果极佳，因此，辛算法与传统的数值解法相比，确有很多优点。 相似文献
20.
We have extend Stormer’s problem considering four magnetic dipoles in motion trying to justify the phenomena of extreme “orderlines”
such as the ones observed in the rings of Saturn; the aim is to account the strength of the Lorentz forces estimating that
the Lorentz field, co-acting with the gravity field of the planet, will limit the motion of all charged particles and small
size grains with surface charges inside a layer of about 200 m thickness as that which is observed in the rings of Saturn.
For this purpose our interest feast in the motion of charged particles with neglected mass where only electromagnetic forces
accounted in comparison to the weakness of the Newtonian fields. This study is particularly difficult because in the regions
we investigate these motions there is enormous three dimensional instability. Following the Poincare’s hypothesis that periodic
solutions are ‘dense’ in the set of all solutions in Hamiltonian systems we try to calculate many families of periodic solutions
and to study their stability. In this work we prove that in this environment charged particles can trace planar symmetric
periodic orbits. We discuss these orbits in details and we give their symplectic relations using the Hamiltonian formulation
which is related to the symplectic matrix. We apply numerical procedures to find families of these orbits and to study their
stability. Moreover we give the bifurcations of these families with families of planar asymmetric periodic orbits and families
of three dimensional symmetric periodic orbits. 相似文献