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  • 1
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of Fluorine Chemistry 29 (1985), S. 67 
    ISSN: 0022-1139
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Chemie 99 (1968), S. 2460-2467 
    ISSN: 1434-4475
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Abstract The method developed for the preparation of tertiary and di-tertiary phosphines by reaction of potassium diphenylphosphide with alkali salts of aromatic sulfonic acids in high-boiling ethers as solvents was applied to the preparation of analogous arsenic compounds. It was possible to prepare in moderate yields some hitherto unknown aromatic arseno compounds. As a side reaction cleavage of the As−C bond yielding metallic arsenic occurs as well as cleavage of the solvent used, β,β′-diethoxydiethylether, with concomitant formation of 1,2-bisdiphenylarsino ethane. The ready reaction of 2 moles potassium diphenylarside with 1 mole sodium 4-chlorobenzenesulfonate leads to 1,4-phenylenebisdiphenyl arsine in high yield.
    Notes: Zusammenfassung Die zur Darstellung tertiärer und ditertiärer Phosphine entwickelte Methode der Umsetzung von Kaliumdiphenylphosphid mit Alkalisalzen aromatischer Sulfonsäuren in hochsiedenden Äthern wurde auf die Darstellung analoger Arsenverbindungen übertragen. Damit konnten einige bisher unbekannte Arsenverbindungen der aromatischen Reihe (in mäßigen Ausbeuten) dargestellt werden, deren Synthese aber auf anderen Wegen kaum durchführbar ist. Als Nebenreaktion tritt eine Spaltung der As−C-Bindung unter Abscheidung von metallischem Arsen und außerdem eine Spaltung des als Lösungsmittel angewendeten β,β′-Diäthoxydiäthyläthers unter Bildung von 1,2-Bisdiphenylarsinoäthan auf. Die Umsetzung von 2 Mol (C6H5)2AsK mit 4-chlorbenzolsulfonsaurem Na aber argab nach kurzer Reaktionszeit das 1,4-Phenylenbisdiphenylarsin in hohen Ausbeuten.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Celestial mechanics and dynamical astronomy 24 (1981), S. 63-82 
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The article describes the solutions near Lagrange's circular collinear configuration in the planar problem of three bodies with three finite masses. The article begins with a detailed review of the properties of Lagrange's collinear solution. Lagrange's quintic equation is derived and several expressions are given for the angular velocity of the rotating frame. The equations of motion are then linearized near the circular collinear solution, and the characteristic equation is also derived in detail. The different types of roots and their corresponding solutions are discussed. The special case of two equal outer masses receives special attention, as well as the special case of two small outer masses. Finally, the fundamental family of periodic solutions is extended by numerical integration all the wap up to and past a binary collision orbit. The stability and the bifurcations of this family are briefly enumerated.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Celestial mechanics and dynamical astronomy 14 (1976), S. 383-392 
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Some properties are derived for the solutions of the variational equations of a class of dynamical systems. It is shown that in rather general conditions the matrix of the linearized Lagrangian equations of motion have an important property for which the word ‘skew-symplectic’ has been introduced. It is also shown that the fundamental matrix of solutions is ‘symplectic’, the word symplectic being used here in a more general sense than in the classical literature. Two consequences of the symplectic property are that the fundamental matrix is easily invertible and that the eigenvalues appear in reciprocal pairs. The effect of coordinate transformations is also analyzed; in particular the change from Lagrangian to canonical systems.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Celestial mechanics and dynamical astronomy 12 (1975), S. 317-325 
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract It is shown that it is possible to make a change of variables in a Lagrangian in such a way that the number of variables is increased. The Euler-Lagrange equations in the redundant variables are obtained in the standard way (without the use of Lagrange Multipliers!). These equations are not independent but they are all valid and consistent. In some cases they are simpler than if the minimum number of variables are used. The redundant variables are supposed to be related to each other by several constraints (not necessarily holonomic), but these constraints are not used in the derivation of the equations of motion. The method is illustrated with the well known Kustaanheimo-Stiefel Regularization. Some interesting applications to perturbation theory are also described.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Celestial mechanics and dynamical astronomy 16 (1977), S. 215-225 
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In the present note we first give a simple proof of the Dainelli formulas for the force field generating a given family of orbits. We also show that the Szebehely partial differential equation for the potential can be derived from the Dainelli formulas if the energy integral is assumed. The Szebehely equation can be solved directly with the method of characteristics or indirectly with the Joukovsky formulas. Several examples are briefly described in the article. In particular we find some rather general potential functions corresponding to circular motion.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Celestial mechanics and dynamical astronomy 18 (1978), S. 3-7 
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The first integral of $$\ddot x = - V\prime (x)$$ yields an integral for the period of a periodic solution, if such exists. In general, this integral cannot be evaluated. By means of an approximate solution along with the minimization of a mean-square error, one can obtain an approximate value for the period in terms of the amplitude of the motion. The calculated period agrees very well with the period obtained by means of numerical integration for the case of orbit-orbit resonance involving the motion of two satellites of a planet. The same method is applied to obtain an alternative derivation of the first Krylov-Bogoliuboff averaging method in non-linear mechanics.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Celestial mechanics and dynamical astronomy 8 (1973), S. 5-10 
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract It is shown that the equations of the general three-body problem take on a very symmetric form when one considers only their relative positions, rather than position vectors relative to some given coordinate system. From these equations one quickly surmises some well known classical properties of the three-body problem such as the first integrals and the equilateral triangle solutions. Some new Lagrangians with relative coordinates are also obtained. Numerical integration of the new equations of motion is about 10 percent faster than with barycentric or heliocentric coordinates.
    Type of Medium: Electronic Resource
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  • 9
    Publication Date: 1975-11-01
    Print ISSN: 0923-2958
    Electronic ISSN: 1572-9478
    Topics: Physics
    Published by Springer
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  • 10
    Publication Date: 1973-08-01
    Print ISSN: 0923-2958
    Electronic ISSN: 1572-9478
    Topics: Physics
    Published by Springer
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