关于一类非线性微分系统周期解的存在性

本文应用映射不动点的方法,研究一类非线性微分系统周期解的存在性,得到了几个结果,并给出应用实例。     

Dynamical causes of asymmetry in the arrangement of gaps in the asteroid belt

The centers of the gaps observed in the asteroid belt are displaced toward Jupiter from their positions that correspond to the exact commensurability between the mean motions of an asteroid and Jupiter. Using the current theory of stability and nonlinear oscillations of Hamiltonian systems, we point out the dynamical causes of this asymmetry. Our analysis is performed in terms of the plane circular restricted three-body problem. The orbits that correspond to Poincaré periodic solutions of the first kind are taken as unperturbed asteroid orbits.     

Classes of Families of Generalized Periodic Solutions to the Beletsky Equation

For the equation describing plane oscillations and rotations of a satellite, we consider families of symmetric generalized periodic solutions with integral rotation number p. We give new confirmations of the hypothesis: there are only four classes of these families with topologically different structures, namely, the classes of families of periodic solutions with p≥ 1, p= 0, p=−1, and p≤−2. Besides, we demonstrate that the vertices of cusps of these families are placed on some analytical curves, and the same is true for the multiple intersections of these families with other families.     

Motion close to the Hopf Bifurcation Of the vertical family of periodic orbits of L4

The paper deals with different kinds of invariant motions (periodic orbits, 2D and 3D invariant tori and invariant manifolds of periodic orbits) in order to analyze the Hamiltonian direct Hopf bifurcation that takes place close to the Lyapunov vertical family of periodic orbits of the triangular equilibrium point L₄ in the 3D restricted three-body problem (RTBP) for the mass parameter, μ greater than (and close to) μ_R (Routh’s mass parameter). Consequences of such bifurcation, concerning the confinement of the motion close to the hyperbolic orbits and the 3D nearby tori are also described.     

The influence of deformation partitioning on dissolution and solution transfer in low-grade tectonic mélange

Abstract Dissolution of quartz and the recryst-allization and re-equilibration of phyllosilicates produce the dark anastomosing seams that dominate microstructures of tectonic melange which occur in a low-grade, imbricated and multiply deformed, mid-Palaeozoic, intracra-tonic fiysch sequence in northeastern Australia. Seams are composed of very closely spaced or coalesced cleavage lamellae, which are very thin layers of extremely fine-grained phyllosilicates. Cleavage seams enclose lenses of silt-stone or greywacke, which formerly occurred in continuous sedimentary layers, indicating extremely heterogeneous and disruptive deformation. Microphacoids enclosed by cleavage seams have subtle shape asymmetries analogous to those of porphyroclasts. Phyllosilicate-preferred orientations within microphacoids commonly lie at a low angle to enclosing seams, and asymmetric relationships occur within seams. The shape and fabric asymmetries appear to be constant, and are regarded as analgous to S and C planes. The number and extent of seams, the amount of dissolution they indicate, and the efficiency of deformation partitioning imply some enhancement of chemical activity and substantial silica loss from the system. This, in turn, suggests the passage of large amount of silica-undersaturated fluid, and melanges may be zones of high fluid flow. However, the microstructures and the disruptive nature of the fabrics may also reflect the influence of high bulk shear strains and suggest some relationship between the shearing component of deformation and the development of cleavages and foliations.     

An analytical solution for a jointed shield‐driven tunnel lining

This paper presents an analytical solution for the prediction of internal forces and displacements of a jointed segmental precast circular tunnel lining. The effects of joint stiffness on the performance of the tunnel lining are discussed. The ‘force method’ is used to determine the internal forces and displacements of jointed tunnel lining. Five shield‐driven tunnel cases are adopted to study the effects of joint stiffness, soil resistance, joint distribution and joint number on the internal forces and displacements of circular tunnels. Laboratory model tests are conducted to verify the proposed analytical solution. Copyright © 2001 John Wiley & Sons, Ltd.     

The planar Hill problem with oblate primary

The regularized equations of motion of the planar Hill problem which includes the effect of the oblateness of the larger primary body, is presented. Using the Levi-Civita coordinate transformation as well as the corresponding time transformation, we obtain a simple regularized polynomial Hamiltonian of the dynamical system that corresponds to that of two uncoupled harmonic oscillators perturbed by polynomial terms. The relations between the synodic and regularized variables are also given. The convenient numerical computations of the regularized equations of motion, allow derivation of a map of the group of families of simple-periodic orbits, free of collision cases, of both the classical and the Hill problem with oblateness. The horizontal stability of the families is calculated and we determine series of horizontally critical symmetric periodic orbits of the basic families g and g'. This revised version was published online in July 2006 with corrections to the Cover Date.     

An Addendum to the Damour and Deruelle's Solution of the Post-Newtonian Two-Body Problem

A complement to the the analytical solution given by Damour and Deruelle (D&D) in order to solve the differential equations that describe the conic-like and rectilinear post-Newtonian two-body problem is presented. We show the geometric relation between the eccentric and true anomalies for the elliptic-like and hyperbolic-like cases and expressions for their velocities are obtained. A post-Newtonian version of the Lambert's theorem is shown. This revised version was published online in July 2006 with corrections to the Cover Date.     

Updated UBV Light-Curve and Period Analysis of Eclipsing Binary HS Herculis

UBV light-curves of the eclipsing binary HS Herculis, obtained in 2002–2003 observational seasons, were analysed with Wilson-Devinney computer code. New absolute dimensions of the system were calculated using the results of the light-curve analysis. Period variation of the system was also investigated. Several new times of minima have been secured for this problematic system. An apsidal motion with a period of 80.7 years was confirmed and a third body in a pretty eccentric orbit (e ₃ = 0.90 ± 0.08) with a period of 85.4 years was found. The corresponding internal structure constants of the binary system, log k ₂, and the mass of the third body were derived.     

Numerical Investigation of the Galactic Problem by Computing Families of Periodic Solutions

The galactic dynamical system expressed by a third-order axisymmetric polynomial potential is investigated numerically by computing periodic solutions. We define as Sthe compact set of initial conditions generating bounded motions, and as S ^p , with S ^p ? S, the countable set of all initial conditions generating periodic solutions. Then, we consider the subsets S _s ^p and S _a ^p of S ^p , where S _s ^p ∪ S _a ^p = S ^p , S _s ^p S _a ^p = Ø, the first of which corresponds to symmetric periodic solutions, and the second to asymmetric solutions. Then, we approximate the set S _s ^p , leaving treatment of the set S _a ^p of asymmetric solutions for a future publication. The set S _s ^p is known to be dense in S (‘Last Geometric Theorem of Poincar;’, Birkhoff, 1913). Using a computer programme capable to locate all elements of the set S _s ^p that generate symmetric periodic solutions that re-enter after intersecting the axis of symmetry from 1 to ntimes. The results of the approximation of S _s ^p in the total domain and in the sample sub-domains of zooming, we present in graphical form as family curves in the (x, C) plane. The solutions located with the largest periods re-enter after 440 galaxy revolutions while the families calculated fully (initial conditions, period, energy, stability co-efficient) include solutions that re-enter after 340 galaxy revolutions. To advance further the approximation of the set S _s ^p thus obtained, we applied the same procedure inside eight sub-domains of the domain Sinto which we ‘zoomed’ through selection of finer search steps and double maximum periods. The family curves thus calculated presented in the (x, C) plane do not intersect anywhere in some sub-domains and their pattern resembles that of laminar flow. In other sub-domains, however, we found family curves from which branching families emanate. The concepts of completeand non-completeapproximation of S _s ^p in sub-domains of laminar and sub-domains with branching family curves, respectively, is introduced. Also, the concept of basic family of order1, 2, ..., n, are defined. The morphology of individual periodic solutions of all families is investigated, and the types of envelopes found are described. The approximate set S _s ^p was also checked by computing Poincar; sections for energy values corresponding to the mean energy range of the eight sub-domains of zooming mentioned above. These sections show that most parts of the compact domain in Sgenerating non-periodic but bounded solutions correspond to with well-shaped tori that intersect the x-axis, a fact that implies that dominant to exclusive type of periodic solutions are the symmetric ones with two normal crossings of this axis. The presence of non-symmetric periodic solutions as well as of chaotic regions is encountered. All calculations reported here were performed using the variable step R-K 8th-order direct integration and setting the allowable energy variation Δ C= |C _start? C _end| < 10^?13. The output, consisting of many thousands of families and their properties (initial conditions, morphology, stability, etc.), is stored in a directory entitled ‘Atlas of the Symmetric Periodic Solution of the Galactic Motion Problem’.