陀螺进动与强迫进动轨道

陀螺进动与轨道进动现象的相似性归因于二者的动力学相似性. 通过类比二者的动力学模型,提出了一类强迫进动轨道. 若以圆轨道为初始轨道,通过施加常值法向力可以实现一种特殊的悬浮型强迫进动轨道. 采用四元数建模方法求解了这种强迫进动轨道的进动规律,给出了解析表达式,据此分析了这种轨道的性质. 分析结果表明这种强迫进动轨道与初始圆轨道在同一球面上,且与初始位置相切. 其角速度为进动角速度与初始轨道角速度的合成,是一种悬浮轨道,即属于非开普勒轨道. 悬浮轨道在地球观测、行星际科学、天文观测、无线电通讯以及地球工程等领域具有潜在应用前景. 从强迫进动的角度出发所作的分析为悬浮轨道的实现提供了一种新途径.     

Negative tunnelling magnetoresistance in spin filtering magnetic junctions with spin-orbit coupling

We present theoretical calculations of spin transport in spin filtering magnetic tunnelling junctions based on the Landauer-Buttiker formalism and taking into account the spin-orbit coupling(SOC).It is shown that spin-flip scattering induced by SOC is stronger in parallel alignment of magnetization of the ferromegnet barrier(FB) and the ferromagnetic electrode than that in antiparallel case.The increase of negative tunnelling magnetoresistance with bias is in agreement with recent experimental observation.     

控制单模激光Haken-Lorenz系统混沌的一种有效方法

基于变量脉冲反馈法(VPF)的设计思想,提出了一种控制非线性系统中混沌的新方法——变量变化率脉冲反馈(VRPF)法.将此方法应用到单模激光Haken-Lorenz系统混沌的控制中,计算机模拟结果表明,通过恰当地选择反馈系数和脉冲间隔,可以将系统稳定在1p、2p、3p…2mp、3np以及2mp×3np这样不同的周期轨道,并且获得同一周期轨道的反馈系数和脉冲间隔并不是唯一的.     

基于ADAMS有轨起重机的非圆轨道修正及动态仿真

为了解决有轨起重机在转弯时,出现的啃轨问题。提出先修正内侧轨道再修正外侧轨道的方法。对于内侧轨道,在直线段和圆弧段轨道加入一段缓和曲线,使曲率半径从无穷大逐渐过渡到圆弧曲率半径;对于外侧轨道,通过四角门框计算出外侧两角点的轨迹。通过求两角点轨迹的中线,即四角门框的外侧轨道,再叠加多轮修正值δ进一步修正外侧轨道。应用Adams进行动态仿真,验证修正轨道是否可以安全通过,并用Adams仿真优化起重机基距、平衡梁尺寸。结果表明,加入的回旋线长度Ls越大,有轨起重机大车在转弯时,出现的偏移量越小。同时,得出有轨起重机平衡梁和基距最优解。     

EXISTENCE OF PERIODIC SOLUTIONS TO A PERTURBED FOUR-DIMENSIONAL SYSTEM

Consider a k multiple closed orbit on an invariant surface of a four dimensional system, after a suitable perturbation, the closed orbit can generate periodic orbits and double-period orbits. Using bifurcation methods and techniques, sufficient conditions for the existence of periodic solutions to the perturbed four dimensional system are obtained, and the period-doubling bifurcations is discussed.     

Leibniz代数胚上动力系统的轨道范例与图示

首先陈述Leibniz代数胚上的动力系统和在局部坐标系下该动力系统的方程,在此基础上,给出了动力系统轨道的范例和图示.     

Similarity of operators associated with the Volterra relation

The “Volterra relation” is the commutation relation [S,V]⊂V ², where S is a not necessarily bounded operator, V is a bounded operator leaving D(S) invariant, and [⋅,⋅] is the Lie product. When S,V are so related, and in addition iS generates a bounded C ₀-group of operators and V has some general property, it is known that S+α V (α∈ℂ) is similar to S if and only if ℜ α=0 (cf. Theorem 11.17 in Kantorovitz, Spectral Theory of Banach Space Operators, Springer, Berlin, 1983). In particular, S−V is not similar to S. However, it is shown in this note that (without any restriction on V and on the group S(⋅) generated by iS), the perturbations (S−V)+P are similar to S for all P in the similarity sub-orbit {S(a)VS(−a);a∈ℝ} of V. When S is bounded, the above perturbations are similar to S for all P in the wider similarity sub-orbit {e ^aS Ve ^−aS ;a∈ℂ}.     

On <Emphasis Type="Italic">δ</Emphasis>-homogeneous Riemannian manifolds. II

We continue the study of the δ-homogeneous Riemannian manifolds defined in a more general case by V. N. Berestovski? and C. P. Plaut. Each of these manifolds has nonnegative sectional curvature. We prove in particular that every naturally reductive compact homogeneous Riemannian manifold of positive Euler characteristic is δ-homogeneous.     

Detecting unstable periodic orbits and unstable quasiperiodic orbits in vibro-impact systems

In this paper, unstable dynamics is considered for the models of vibro-impact systems with linear differential equations coupled to an impact map. To provide a skeleton for the organization of chaotic attractors, we propose a method for detecting unstable periodic orbits embedded in chaotic attractors through a combination of unconstrained optimization technique and Poincaré map. Three numerical examples from different vibro-impact models demonstrate that the strategy can efficiently detect unstable periodic orbits in chaotic attractors. In order to explore the mechanism responsible for the creation of multi-dimensional tori attractors, we also present another method to detect unstable quasiperiodic orbits embedded multi-dimensional tori attractors by examining a specially transient time series. The upper bound and lower bound of the transient time series (in the Poincaré map) can be obtained by analyzing transient Lyapunov exponent and transient Lyapunov dimension. Some examples verify the effectiveness of the numerical algorithm.     

A criticality result for polycycles in a family of quadratic reversible centers

We consider the family of dehomogenized Loud's centers $X_{\mu }=y(x?1){?}_x+(x+D{x}^2+F{y}^2){?}_y$, where $\mu =(D,F)\in {\mathbb{R}}^2$, and we study the number of critical periodic orbits that emerge or disappear from the polycycle at the boundary of the period annulus. This number is defined exactly the same way as the well-known notion of cyclicity of a limit periodic set and we call it criticality. The previous results on the issue for the family $\{X_{\mu },\mu \in {\mathbb{R}}^2\}$ distinguish between parameters with criticality equal to zero (regular parameters) and those with criticality greater than zero (bifurcation parameters). A challenging problem not tackled so far is the computation of the criticality of the bifurcation parameters, which form a set ${\mathrm{\Gamma }}_B$ of codimension 1 in ${\mathbb{R}}^2$. In the present paper we succeed in proving that a subset of ${\mathrm{\Gamma }}_B$ has criticality equal to one.