1,721,346 research outputs found
The Ermanno-Bernoulli constants and representations of the complete symmetry group of the Kepler Problem
No full textThe expression of the components of the equation of motion of the classical Kepler problem in terms of the natural variables associated with the Ermanno-Bernoulli constants leads naturally to the same equations as are obtained by the technique of reduction of order developed by Nucci [J. Math. Phys. 37, 1772 (1996)], reported by Nucci and Leach [J. Math. Phys. 42, 746 (2001)]. Three representations of the complete symmetry group of the Kepler problem are obtained from the three standard representations of the complete symmetry group of the simple harmonic oscillator. The algebra of the complete symmetry group of the two-dimensional Kepler problem is identified to be A(1)circle plus{A(3,3)}. The applicability of the results to other classes of problem, such as the Kepler problem with drag, which possess a conserved vector of Laplace-Runge-Lenz type, is indicated. The three-dimensional Kepler problem is shown to be completely specified by six symmetries rather than the eight previously reported by Krause [J. Math. Phys. 35, 5734 (1994)]
The harmony in the Kepler and related problems
No full textThe technique of reduction of order developed by Nucci [J. Math. Phys. 37, 1772-1775 (1996)] is used to produce nonlocal symmetries in addition to those reported by Krause [J. Math. Phys. 35, 5734-5748 (1994)] in his study of the complete symmetry group of the Kepler problem. The technique is shown to be applicable to related problems containing a drag term which have been used to model the motion of low altitude satellites in the Earth's atmosphere and further generalizations. A consequence of the application of this technique is the demonstration of the group theoretical relationship between the simple harmonic oscillator and the Kepler and related problems
Jacobi's last multiplier and the complete symmetry group of the Euler-Poinsot system
No full textThe symmetry approach to the determination of Jacobi's last multiplier is inverted to provide a source of additional symmetries for the EulerPoinsot system. These addtional symmetries are nonlocal. They provide the symmetries for the representation of the complete symmetry group of the system
The ladder problem: Painleve' integrability and explicit solution
No full textWe consider the n-dimensional ladder system, that is the homogeneous quadratic system of first-order differential equations of the form (x)over dot (i) = x(i) Sigma(j=1)(n) a(ij)xj, i = 1, n, where (a(ij)) = (i + j), i, j = 1, n, introduced by Imai and Hirata (2002 Preprint nlin.SI/0212007 v1 3). The ladder system is found to be integrable for all n in terms of the Painleve analysis and its solution is explicitly given
Symmetry analysis of and first integrals for the continuum Heisenberg spin chain
No full textDaniel et al. [6] analysed the singularity structure of the continuum limit of the one-dimensional anisotropic Heisenberg spin chain in a transverse field and determined the conditions under which the system is nonintegrable and exhibits chaos. We investigate the governing differential equations for symmetries and find the associated first integrals. Our results complement the results of Daniel et al
The determination of nonlocal symmetries by the technique of reduction of order
No full textAutonomous systems of ordinary differential equations can be rewritten as systems of first order ordinary differential equations and one of the dependent variables chosen as a new independent variable. Some of the variables are eliminated to give a mixed system of first and second order equations for which the determination of point symmetries can be automated without having to make an Ansatz on the detailed structure of the symmetry. Because the coefficient function for the original independent variable appears only as its derivative in the reduced system, symmetries which are nonlocal in this variable become local symmetries of the reduced system and can be computed algorithmically
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
The duty to investigate right to life violations across three regional systems: harmonisation or fragmentation of international human rights law?
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