共查询到20条相似文献，搜索用时 31 毫秒
1.
Taeyoung Lee Melvin Leok N. Harris McClamroch 《Celestial Mechanics and Dynamical Astronomy》2007,98(2):121-144
Equations of motion, referred to as full body models, are developed to describe the dynamics of rigid bodies acting under
their mutual gravitational potential. Continuous equations of motion and discrete equations of motion are derived using Hamilton’s
principle. These equations are expressed in an inertial frame and in relative coordinates. The discrete equations of motion,
referred to as a Lie group variational integrator, provide a geometrically exact and numerically efficient computational method
for simulating full body dynamics in orbital mechanics; they are symplectic and momentum preserving, and they exhibit good
energy behavior for exponentially long time periods. They are also efficient in only requiring a single evaluation of the
gravity forces and moments per time step. The Lie group variational integrator also preserves the group structure without
the use of local charts, reprojection, or constraints. Computational results are given for the dynamics of two rigid dumbbell
bodies acting under their mutual gravity; these computational results demonstrate the superiority of the Lie group variational
integrator compared with integrators that are not symplectic or do not preserve the Lie group structure. 相似文献
2.
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
3.
Modeling the effects of atmospheric drag is one of the more important problems associated with the determination of the orbit of a near-earth satellite. Errors in the drag model can lead to significant errors in the determination and prediction of the satellite motion. The uncertainty in the drag acceleration can be attributed to three separate effects: (a) errors in the atmospheric density model, (b) errors in the ballistic coefficient, and (c) errors in the satellite relative velocity. In a number of contemporary satellite missions, the requirements for performing the orbit determination and predictions in near real-time has placed an emphasis on density model computation time as well as the model accuracy. In this investigation, a comparison is made of three contemporary atmospheric density models which are candidates for meeting the current orbit computation requirements. The models considered are the analytic Jacchia-Roberts model, the modified Harris-Priester model, and the USSR Cosmos satellite derived density model. The computational characteristics of each of the models are compared and a modification to the modified Harris-Priester model is proposed which improves its ability to represent the diurnal variation in the atmospheric density.This investigation was supported by the NASA Goddard Spaceflight Center under contract NAS5-20946 and Contract NSG 5154. 相似文献
4.
The paper presents an efficient algorithm for the study of satellite and space debris orbits on long time intervals. The averaged equations of motion are integrated by means of the implicit midpoint method. This approach is known as a symplectic mapping technique. The perturbing forces included in the mapping are: the geopotential, the atmospheric drag, lunisolar perturbations and the direct radiation pressure (without shadow effects). The influence of the atmosphere is approximated by simple methods for the estimation of integrals. The described mapping is valid for the wide range of orbits including the resonant and the eccentric ones; it can be helpful in practical and theoretical problems. The lifetime of GPS transfer orbits is discussed as an exemplary application. 相似文献
5.
J. S. Watson G. D. Mistretta N. L. Bonavito 《Celestial Mechanics and Dynamical Astronomy》1975,11(2):145-177
In order to retain separability in the Vinti theory of Earth satellite motion when a nonconservative force such as air drag is considered, a set of variational equations for the orbital elements are introduced, and expressed as functions of the transverse, radial, and normal components of the nonconservative forces acting on the system. In this approach, the Hamiltonian is preserved in form, and remains the total energy, but the initial or boundary conditions and hence the Jacobi constants of the motion advance with time through the variational equations. In particular, the atmospheric density profile is written as a fitted exponential function of the eccentric anomaly, which adheres to tabular data at all, altitudes and simultaneously reduces the variational equations to definite integrals with closed form evaluations whose limits are in terms of the eccentric anomaly. The values of the limits for any arbitrary time interval are obtained from the Vinti program.Results of this technique for the case of the intense air drag satellites San Marco-2 and Air Force Cannonball are given. These results indicate that the satellite ephemerides produced by this theory in conjunction with the Vinti program are of very high accuracy. In addition, since the program is entirely analytic, several months of ephemerides can be obtained within a few seconds of computer time. 相似文献
6.
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
7.
Patrick Michel Giovanni H. Valsecchi 《Celestial Mechanics and Dynamical Astronomy》1996,65(4):355-371
We discuss the efficiency of the so-called mixed-variable symplectic integrators for N-body problems. By performing numerical experiments, we first show that the evolution of the mean error in action-like variables is strongly dependent on the initial configuration of the system. Then we study the effect of changing the stepsize when dealing with problems including close encounters between a particle and a planet. Considering a previous study of the slow encounter between comet P/Oterma and Jupiter, we show that the overall orbital patterns can be reproduced, but this depends on the chosen value of the maximum integration stepsize. Moreover the Jacobi constant in a restricted three-body problem is not conserved anymore when the stepsize is changed frequently: over a 105 year time span, to keep a relative error in this integral of motion of the same order as that given by a Bulirsch-Stoer integrator requires a very small integration stepsize and much more computing time. However, an integration of a sample including 104 particles close to Neptune shows that the distributions of the variation of the elements over one orbital period of the particles obtained by the Bulirsch-Stoer integrator and the symplectic integrator up to a certain integration stepsize are rather similar. Therefore, mixed-variable symplectic integrators are efficient either for N-body problems which do not include close encounters or for statistical investigations on a big sample of particles. 相似文献
8.
In this paper, a new family of explicit and implicit multistep methods is presented both for the error-controlled and uncontrolled modes. The main concept is to replace the Newton interpolation with the Hermite interpolation, where the Hermite polynomial is fitted to the function values and its derivatives. This idea is very useful in the numerical solution of problems (e.g., orbit propagation problem) where higher-order derivatives can easily be computed. In addition to the theoretical concept, the stability regions of the proposed methods are determined. The new methods are more stable than the well-known multistep numerical integrators (i.e., Adams–Bashforth and Adams–Bashforth–Moulton) in the explicit, implicit, and predictor–corrector forms. Using the second-order derivatives gives smaller error constants in the proposed method. The new integrators are numerically tested for a few examples, and the solutions are compared with those of the well-known multistep methods. Moreover, the CPU time and absolute integration error are compared in the satellite orbit propagation problem using various integration methods. The CHAMP mission, i.e., a German small-satellite mission for geoscientific and atmospheric research and applications, is considered as a case study for comparing the achievable accuracy of the proposed method with the existing method for solving the two-body problem. 相似文献
9.
An Implementation of the Logarithmic Hamiltonian Method for Artificial Satellite Orbit Determination
Seppo Mikkola Phil Palmer Yoshi Hashida 《Celestial Mechanics and Dynamical Astronomy》2002,82(4):391-411
We discuss the use of a recently discovered exact two-body leapfrog for accurate symplectic integration of perturbed two-body motion and for the computation of the state-transition matrix. We pay special attention to artificial satellite orbit determination and describe in detail the evaluation of the perturbing acceleration. Inclusion of air drag and other non-canonical forces are also discussed. The main advantage of this new formulation is conceptual simplicity, for easy programming and high accuracy for orbits with large eccentricity. The method has been evaluated in real artificial satellite orbit determinations.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
10.
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
11.
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
12.
Vladimir Martinusi Lamberto Dell’Elce Gaëtan Kerschen 《Celestial Mechanics and Dynamical Astronomy》2017,127(4):451-476
The paper offers the fully analytic solution to the motion of a satellite orbiting under the influence of the two major perturbations, due to the oblateness and the atmospheric drag. The solution is presented in a time-explicit form, and takes into account an exponential distribution of the atmospheric density, an assumption that is reasonably close to reality. The approach involves two essential steps. The first one concerns a new approximate mathematical model that admits a closed-form solution with respect to a set of new variables. The second step is the determination of an infinitesimal contact transformation that allows to navigate between the new and the original variables. This contact transformation is obtained in exact form, and afterwards a Taylor series approximation is proposed in order to make all the computations explicit. The aforementioned transformation accommodates both perturbations, improving the accuracy of the orbit predictions by one order of magnitude with respect to the case when the atmospheric drag is absent from the transformation. Numerical simulations are performed for a low Earth orbit starting at an altitude of 350 km, and they show that the incorporation of drag terms into the contact transformation generates an error reduction by a factor of 7 in the position vector. The proposed method aims at improving the accuracy of analytic orbit propagation and transforming it into a viable alternative to the computationally intensive numerical methods. 相似文献
13.
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
14.
The axisymmetric satellite problem including radiation pressure and drag is treated. The equations of motion of the satellite are derived. The energy-like and Laplace-like invariants of motion have been derived for a general drag force function of the polar angle, and the Laplace-like invariant is used to find the orbit equation in the case of a spherical satellite. Then using the small parameter, the orbit of the satellite is determined for an axisymmetric satellite. 相似文献
15.
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
16.
Theory of the motion of an artificial Earth satellite 总被引：1，自引：0，他引：1
Felix R. Hoots 《Celestial Mechanics and Dynamical Astronomy》1981,23(4):307-363
An improved analytical solution is obtained for the motion of an artificial Earth satellite under the combined influences of gravity and atmospheric drag. The gravitational model includes zonal harmonics throughJ
4, and the atmospheric model assumes a nonrotating spherical power density function. The differential equations are developed through second order under the assumption that the second zonal harmonic and the drag coefficient are both first-order terms, while the remaining zonal harmonics are of second order.Canonical transformations and the method of averaging are used to obtain transformations of variables which significantly simplify the transformed differential equations. A solution for these transformed equations is found; and this solution, in conjunction with the transformations cited above, gives equations for computing the six osculating orbital elements which describe the orbital motion of the satellite. The solution is valid for all eccentricities greater than 0 and less than 0.1 and all inclinations not near 0o or the critical inclination. Approximately ninety percent of the satellites currently in orbit satisfy all these restrictions. 相似文献
17.
Ch. Tsitouras 《Celestial Mechanics and Dynamical Astronomy》1999,74(4):223-230
A tenth order explicit symmetric and in consequence symplectic Runge–Kutta–Nyström method is presented here. We derive the order conditions needed and solve them for the parameters of the method. Numerical results indicate the superiority of the new method compared to the other high order symplectic methods appeared in the literature until now. 相似文献
18.
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
19.
This paper studies libration dynamics and stability of deorbiting nano-satellites by short and bare electrodynamic tethers. A critical aspect of satellite deorbit by an electrodynamic tether is to maintain the tether aligned with the local vertical and stable while subjected to external perturbations. The dynamics of electrodynamic tether system in deorbit application is divided into the orbital motion of the center of system’s mass and the tether libration motion relative to that center. Major space environmental perturbations including the current-induced electrodynamic force, atmospheric drag, oblateness effect of the Earth, irregularity of geomagnetic field, variable plasma density, solar radiation pressure, and lunisolar gravitational attractions are considered in the dynamic analysis. Quantitative analyses are provided in order to characterize the order of the perturbative torques during the deorbit process. A single index is derived from the libration energy to stabilize the libration motion by regulating the current in the tether through simple on-off switching. Numerical results show that the libration dynamics of an electrodynamic tether has significant impacts on the deorbit process and the electrodynamic tether cannot effectively deorbit satellites without libration stability control. The proposed current regulation strategy is simple and very effective in stabilizing libration motion of an electrodynamic tether. 相似文献
20.
Equations are presented for the computation of tangent maps for use in nearly Keplerian motion, approximated by use of a symplectic
leapfrog map. The resulting algorithms constitute more accurate and efficient methods to obtain the Liapunov exponents and
the state transition matrix, and can be used to study chaos in planetary motions, as well as in orbit determination procedures
from observations. Applications include planetary systems, satellite motions and hierarchical, nearly Keplerian systems in
general.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献