Boundary curves for families of planar orbits

For monoparametric familiesf(x,y)=c of planar orbits, created by a planar potentialV(x,y), we introduce the notion of the family boundary curves (FBC). All members of the familyf(x,y)=c are traced in an allowable region of thexy plane, defined by the corresponding FBC, with total energyE=E(c) varying along the family. Family boundary curves are also found for two-parametric familiesf(x,y,b)=c. The relation of equilibrium points and asymptotic orbits, possibly possessed by the potentialV(x,y), to be FBC is studied.     

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.     

Isolated Periodic Orbits and Stability in Separable Potentials

A method for determining the main families of isolated periodic orbits and their characteristic exponents in planar potentials which are separated by a point transformation is proposed. Since these orbits are continued analytically with the same stability, these results are persistent under small perturbations. The method is applied to the two fixed centers problem, the Paul trap and the dipole expansion of an electrostatic potential. This revised version was published online in July 2006 with corrections to the Cover Date.     

The family I3υ of the three-dimensional general three-body problem (Parts I and II)

We present the biparametric family I_3υ of symmetric periodic orbits of the three-dimensional general three-body problem, found by numerical continuation of the vertical critical orbit I_3υ of the circular restricted three-body problem. The periodic orbits refer to a suitably chosen rotating frame of reference.     

General three-body problem: Families of vertical critical periodic orbits

In this paper we present four families of vertical critical periodic orbits found by continuation, with respect to the small massm ₃, of the vertical critical periodic orbitsl1v, ilv, mlv, c3v of the circular restricted problem. The periodic orbits refer to a suitably defined rotating frame of reference.     

Second-order resonant heave,roll and pitch motions of a deep-draft semi-submersible: Theoretical and experimental results

Large volume semi-submersible units may present significant wave induced resonant motions in heave, roll and pitch. Evaluating the slow motions of such systems is important from the initial stages of their designs and therefore requires a model that is both accurate and expedite enough. In the present article, different options for modeling the second-order hydrodynamic forces and induced motions are discussed using as a case-study the PETROBRAS 52 unit—P-52. Computations of the low frequency forces are performed in the frequency domain by means of a commercial Boundary Element Method (BEM) code. Different hydrodynamic approximations are tested and evaluated by directly comparing the predicted responses with those measured in small-scale tests performed in a wave-basin. From the results obtained in theses comparisons, a methodology based on a white-noise approach of the force spectrum is proposed. The validity of such approximation is attributable to the typically low damping levels in heave, roll and pitch motions. Furthermore, results also indicate that the second order forces may be calculated disregarding the free-surface forcing components, an option that helps to reduce the computational burden even more, rendering the procedure suitable for preliminary design calculations.     

Application of high-order Runge-Kutta methods in the magnetic-binary problem

Our intention in this paper is to present the results obtained from a systematic comparative study of several high-order Runge-Kutta methods as applied in a composite problem of celestial dynamics, namely the magnetic-binary problem.     

Epithermal gold mineralisation in the active Aegean Volcanic Arc: the Profitis Ilias deposit, Milos Island, Greece

The Profitis Ilias gold deposit, located on the western part of Milos Island, Greece, is the first epithermal gold deposit discovered in the Pliocene–Pleistocene Aegean volcanic arc. Estimated ore reserves are 5 million tonnes grading 4.4 g/tonne Au and 43 g/tonne Ag. The deposit is closely associated with a horst and graben structure, and occurs in a series of steep interconnected crustiform-banded quartz veins up to 3 m wide, extending to depths of at least 300 m. The mineralisation occurs in three stages and is hosted by 3.5–2.5 Ma old silicified and sericitised rhyolitic lapilli-tuffs and ignimbrites. It consists of pyrite, galena, chalcopyrite, electrum and native gold. Additionally, adularia occurs with quartz mainly in veins. Homogenisation temperatures of primary liquid-rich inclusions vary from 145 to 399 °C for the ore stage, and 112 to 263 °C for the post-ore stage. Salinities range between 0.1 and 11.4 wt% NaCl equiv. and 0.93 to 8.5 wt% NaCl equiv. for the ore stage and the post-ore stage, respectively. Rare vapour-rich inclusions in ore stage quartz homogenise between 368 and 399 °C and estimates of eutectic melting (−25 to −38 °C) indicate the presence of Ca and Mg in the ore fluids. Sample elevation versus fluid inclusion T_h–salinity relationships show (1) a high-salinity trend, where moderate-temperature (300–250 °C) and moderate-salinity brines (∼3 wt% NaCl equiv.) trend to high-salinity (up to 15 wt% NaCl equiv.) fluids with lower (∼25–50 °C) homogenisation temperatures, and (2) a high-T_h trend where moderate-salinity and moderate-temperature brines (200–250 °C; 3 wt% NaCl equiv.) develop into low-salinity (<1 wt% NaCl equiv.), high-temperature (>350 °C) fluids. These trends are best explained by extreme boiling and vapourisation phenomena between 200 and 250 °C. The 430–450 m asl (metres above sea level) level marks the transition between a lower liquid-dominated segment of the system where only the steep high-salinity trend is seen, and an upper vapour-dominated segment where the high-T_h trend or a combination of both are seen. There is a close spatial association between mineable gold grades and the upper segment of the system. Depth-to-boiling curves suggest that the paleo-surface was ∼200 m above the present summit of Profitis Ilias. Comparison of the mineralisation and fluid geochemistry at Profitis Ilias with that of the nearby modern geothermal system indicates that the processes of metal mineralisation have probably been continuous since the Late Pliocene. Received: 24 February 2000 / Accepted: 15 July 2000     

Periodic orbits in three-dimensional planetary systems

Three-dimensional planetary systems are studied, using the model of the restricted three-body problem for Μ =.001. Families of three-dimensional periodic orbits of relatively low multiplicity are numerically computed at the resonances 3/1, 5/3, 3/5 and 1/3 and their stability is determined. The three-dimensional orbits are found by continuation to the third dimension of the vertical critical orbits of the corresponding planar problem     

An application of the scaled Runge-Kutta algorithms to some problems of celestial mechanics

New Runge-Kutta algorithms are applied for determining the solution of a system of ordinary differential equations at any point within a given integrating step. In this paper we propose the application of these new algorithms in order to determine, with the smallest possible cost, the exact point of intersection of a symmetric orbit, with the axis or plane of symmetry, which appear in various problems of celestial mechanics.