Two-Parametric Families of Orbits and Multiseparability of Planar Potentials

Combining the results of the inverse problem of dynamics with the theory of multiseparability of planar potentials, we find biparametric families of orbits, whose existence guarantees the multiseparability of the potential. We also study the allowed regions of the plane, where these orbits are traced.     

Geometric Derivation of the Delaunay Variables and Geometric Phases

We derive the classical Delaunay variables by finding a suitable symmetry action of the three torus T³ on the phase space of the Kepler problem, computing its associated momentum map and using the geometry associated with this structure. A central feature in this derivation is the identification of the mean anomaly as the angle variable for a symplectic S ¹ action on the union of the non-degenerate elliptic Kepler orbits. This approach is geometrically more natural than traditional ones such as directly solving Hamilton–Jacobi equations, or employing the Lagrange bracket. As an application of the new derivation, we give a singularity free treatment of the averaged J ₂-dynamics (the effect of the bulge of the Earth) in the Cartesian coordinates by making use of the fact that the averaged J ₂-Hamiltonian is a collective Hamiltonian of the T³ momentum map. We also use this geometric structure to identify the drifts in satellite orbits due to the J ₂ effect as geometric phases.     

Deformation styles as a key for interpreting glacial depositional environments

Lithostratigraphical and lithofacies approaches used to interpret glacial sediments often ignore deformation structures that can provide the key to environment of formation. We propose a classification of deformation styles based on the geometry of structures rather than inferred environment of formation. Five styles are recognised: pure shear (P), simple shear (S), compressional (C), vertical (V) and undeformed (U). These dictate the first letter of the codes; the remaining letters conveying the evidence. This information can be used to reconstruct palaeostress fields and to infer physical properties of sediments when they deformed. Individual structures are not diagnostic of particular environments but the suite of structures, their relative scale, stratigraphical relationships, and orientation relative to palaeoslopes and to palaeoice‐flow directions can be used to infer the environment in which they formed. This scheme is applied at five sites in west Wales. The typical succession is interpreted as subglacial sediments overlain by meltout tills, flow tills and sediment flows. Paraglacial redistribution of glacial sediments is widespread. Large‐scale compressional deformation is restricted to sites where glaciers readvanced. Large‐scale vertical deformation occurs where water was locally ponded near the ice margin. There is no evidence for glaciomarine conditions. Copyright © 2003 John Wiley & Sons, Ltd.     

Structural Evolution of the Eastern Margin of Eurasia in Late Mesozoic and Cenozoic

This paper features the structural evolution of the eastern margin of Eurasia in Late Mesozoic and Cenozoic.It is characterized by three stages of development: the riftogenic stage (Jurassic-Early Cretaceous), the platform stage (Late Cretaceous) and the neotectonic one (Paleogene-Quarternary). The boundaries between these stages are distinctly fixed by the geological time limits of planetary range. It is demonstrated that the riftogenic and neotectonic stages were characterized by a high degree of geodynamic activity, and the platform one by a decrease in contrast of tectonic movements. The main river net was formed in the Early Cretaceous and in the Neogene. It experienced a serious reconstruction accompanied by the formation of the Amur River valley being similar to the modem one.     

A Solution of Einstein's Field Equations fora Tachyonic Gas: Possible Astrophysical Applications

In this paper we show that a change in the signs of some of the metric components of the solution of the field equations for the classical cosmic string results in a solution which we interpret as a time-dependent wall composed of tachyons. We show that the walls have the property of focusing the paths of particles which pass through them. As an illustration of this focusing, we demonstrate the results of a simple simulation of the interaction between one such tachyon wall and a rotating disk of point masses. This interaction leads to the temporary formation of spiral structures. These spiral structures exist for a time on the order of one galactic rotation. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Model of the Spraying of Drops from the Molten Surface of a Meteoroid in the Process of Ablation

An additional investigation has been carried out of the rational model (Aslanov, 2000) of the separation of drops from the tops of the unstable wave formation on the molten surface of a meteoroid. The ratio of the wavelength of unstable hydrodynamic disturbances to the diameter of drops has been calculated in a mathematically closed form. Particular theoretical estimates of the size of the region of spraying of molten drops agree with prevailing sizes given in the known classification of the forms of meteoroid fragmentation.