Existence of formal integrals of symplectic integrators     

Xinhao Liao  Lin Liu 《Celestial Mechanics and Dynamical Astronomy》1995,63(1):113-123

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   

On a class of variational equations transformable to the Gauss hypergeometric equation     

Haruo Yoshida 《Celestial Mechanics and Dynamical Astronomy》1992,53(2):145-150

A new class of linear ordinary differential equations with periodic coefficients is found which can be transformed to the Gauss hypergeometric equation, and therefore the monodromy matrices are computable explicitly. These equations appear as the variational equations around a straight-line solution in Hamiltonian systems of the form H = T(p) + V(q), where T(p) and V(q) are homogeneous functions of p and q, respectively.  相似文献   

Analytic continuation of quasi-periodic orbits from non-linear periodic modes     

Michael E. Hough 《Celestial Mechanics and Dynamical Astronomy》1993,57(4):587-617

A new theory is formulated for the analytic continuation of quasi-periodic orbits from non-linear, periodic modes of a two degree-of-freedom system in rotating coordinates. Formal solutions of the equations of motion are developed in series expansions, with the non-linear modes as reference solutions. Conditions are determined on the existence and boundedness of the time-dependent coefficients of the velocity field. Boundedness properties of the orbits are specified by an orbit function derived from the Jacobi integral.  相似文献   

Jarosite stability on Mars     

Alexandra Navrotsky  Ferenc Lázár Forray 《Icarus》2005,176(1):250-253

Jarosite, a potassium (sodium) iron sulphate hydrated mineral, has recently been identified on the martian surface by the Opportunity rover. Using recent thermochemical data [Drouet and Navrotsky, 2003, Geochim. Cosmochim. Acta 67, 2063-2076; Forray et al., 2005, Geochim. Cosmochim. Acta, in press], we calculate the equilibrium decomposition curve of jarosite and show that it is thermodynamically stable under most present martian pressures and temperatures. Its stability makes jarosite potentially useful to retain textural, chemical, and isotopic evidence of past history, including possible biological activity, on Mars.  相似文献   

Multiple resonance in one problem of the stability of the motion of a satellite relative to the center of mass     

A. P. Markeev 《Astronomy Letters》2005,31(9):627-633

We investigate the stability of the periodic motion of a satellite, a rigid body, relative to the center of mass in a central Newtonian gravitational field in an elliptical orbit. The orbital eccentricity is assumed to be low. In a circular orbit, this periodic motion transforms into the well-known motion called hyperboloidal precession (the symmetry axis of the satellite occupies a fixed position in the plane perpendicular to the radius vector of the center of mass relative to the attractive center and describes a hyperboloidal surface in absolute space, with the satellite rotating around the symmetry axis at a constant angular velocity). We consider the case where the parameters of the problem are close to their values at which a multiple parametric resonance takes place (the frequencies of the small oscillations of the satellite’s symmetry axis are related by several second-order resonance relations). We have found the instability and stability regions in the first (linear) approximation at low eccentricities.  相似文献   

地震过程中地形变的Lyapunov指数变化     

张永志 《大地测量与地球动力学》1993,(3)

Lyapunov指数是判断动力学系统演化趋势的主要依据之一。本文根据Lyapunov指数的定义,导出了形变能到达临界状态时地壳中弹性模量与应变状态之间的关系,计算了青海门源6.4级地震过程中不同弹性模量所对应的Lyapunov指数,得出以下结论:(1)在Lyapunov指数稳定的意义下形变能的稳定性与应变张量ε和弹性矩阵D的乘积有关,当2ε~TD大于单位矩阵I时,形变能随应变的变化不稳定;当2ε~TD小于单位矩阵I时,形变能系统稳定。(2)在门源6.4级地震过程中,震后弹性地形变动力学系统的稳定性大于震前的稳定性。  相似文献   

On one special case of parametric resonance in problems of celestial mechanics     

A. P. Markeev 《Astronomy Letters》2005,31(5):350-356

We consider a periodic (in time) linear Hamiltonian system that depends on a small parameter. At a zero value of this parameter, the matrix of the system is constant, has two identical pairs of purely imaginary roots, and is not reducible to diagonal form. Therefore, the unperturbed system is unstable. We propose an algorithm for determining the boundaries of the instability regions for the system at nonzero values of the small parameter. This algorithm was used to analyze the stability of triangular libration points in the elliptical restricted three-body problem and in the stability problem in one special case of stationary rotation of a satellite relative to the center of mass.  相似文献   

黄河积石峡水库I号滑体变形趋势分析     

毛彦龙  彭建兵  梁伟 《地球科学与环境学报》1996,(4)

通过对黄河积石峡水库库外Ｉ＃滑坡体变形趋势分析，认为该滑坡在地震及水雾影响下是稳定的，但稳定系数变动在＂１＂左右，从水工建筑物的安全角度来看是不符合要求的，需要进行治理。  相似文献   

渗流场与应力场耦合分析在地质科学中的应用     

徐则民  张塞  杨立中  刘丹 《国土资源》1996,(3)

本文论述了修流场与应力场耦合分析的基本原理及其在石油勘探、成矿预测及斜坡稳定性评价中应平的理论基础和技术路线．  相似文献   

CINRAD/SA雷达伺服系统稳定性对数据质量的影响     

曹德煜  周红根  江海洋  许波  陈伟伟  赵宇  马雷 《气象科技》2018,46(3):436-442

本文分析CINRAD/SA雷达伺服系统运行不稳定,主要有雷达方位俯仰定位超限、跳变、伺服故障等原因,造成雷达回波异常,并将回波异常分为3类。研究从雷达基数据中检测出雷达伺服系统方位俯仰的定位超限、跳变、故障等质控判别方法,及时发现雷达存在的异常回波问题,推送预警短信,指导台站及时进行维护维修,从而在源头上控制由于雷达伺服系统原因造成的异常回波资料生成,提升雷达数据和产品质量。  相似文献