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8. Commission 38: Exchange of Astronomers (Echange Des Astronomes) (Commission of the Executive Committee)

Author

Jorgensen, H. E., primary, Roberts, M. S., additional, Chitre, D. M., additional, Ducati, J. R., additional, Krisna, G., additional, Morimoto, M., additional, West, R. M., additional, Sahade, J., additional, Al-Sabti, A. A., additional, Boyarchuk, A. A., additional, Caccin, B., additional, Florsch, A., additional, Haupt, H. F., additional, Kondo, Y., additional, Kozai, Y., additional, Leung, D. A., additional, MacRae, D. A., additional, Marik, M., additional, Nha, I.-S., additional, Ninkovic, S., additional, Okoye, S. E., additional, Routly, P. M., additional, Smith, G. F., additional, Su, H.-J., additional, Swarup, G., additional, Tolbert, C. R., additional, van den Heuvel, E. P., additional, Wang, S.-G., additional, Wood, F. B., additional, and Ye, S.-H., additional

Published
1997
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17. Close Binary Stars

Author

Koch, R. H., primary, Piirola, V., additional, Gibson, D. M., additional, Gregory, P. C., additional, Kwok, S., additional, Seaquist, E. R., additional, Kondo, Y., additional, McCluskey, G. E., additional, Leung, Kam-Ching, additional, Hilditch, R. W., additional, Hill, G., additional, Popper, Daniel M., additional, Wright, K. O., additional, Faraggiana, R., additional, Henrichs, H. F., additional, van den Heuvel, E. P. J., additional, Wood, D. B., additional, Budding, E., additional, and Al-Naimiy, H., additional

Published
1977
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18. Close Binary Stars

Author

Larsson-Leander, G., primary, Koch, R. H., additional, Batten, A. H., additional, Cherepaschuk, A. M., additional, Kondo, Y., additional, Gibson, D. M., additional, Herczeg, T., additional, Kitamura, M., additional, Hilditch, R., additional, Rucinski, S. M., additional, Smak, J., additional, van den Heuvel, E. P. J., additional, and Warner, Brian, additional

Published
1982
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22. Close Binary Stars (Etoiles Doubles Serrees)

Author

Warner, B., primary, Herczeg, T., additional, Batten, A., additional, Cherepashchuk, A. M., additional, Kondo, Y., additional, Gibson, D. M., additional, Kitamura, M., additional, Plavec, M., additional, Whelan, J. A. J., additional, van den Heuvel, E. P. J., additional, Gyldenkerne, K., additional, Hall, D. S., additional, and Larsson-Leander, G., additional

Published
1979
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27. Nonlinear Oscillators.

Author

Burton, W. B., Kuijpers, J. M. E., Bertola, F., Cassinelli, J. P., Cesarsky, C. J., Ehrenfreund, P., Engvold, O., Heck, A., Kaspi, V. M., Murdin, P. G., Pacini, F., Radhakrishnan, V., Shu, F. H., Somov, B. V., Sunyaev, R. A., Van Den Heuvel, E. P. J., Van Der Laan, H., and Ferraz-Mello, Sylvio

Abstract

A quasiharmonic Hamiltonian system is a system whose unperturbed part H0(J) is a linear function of the actions. That is, 10.1$$ H = \sum\limits_{i = 1}^N {w_i } J_i + R(q,J,\varepsilon ), $$ where ωi = const and R is a 2π-periodic function of the angles θi, analytical in ε and vanishing for ε = 0. This system is a paradigm of many conservative nonlinear systems. [ABSTRACT FROM AUTHOR]

Published
2007
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28. Lie Series Theory for Resonant Systems.

Author

Burton, W. B., Kuijpers, J. M. E., Bertola, F., Cassinelli, J. P., Cesarsky, C. J., Ehrenfreund, P., Engvold, O., Heck, A., Kaspi, V. M., Murdin, P. G., Pacini, F., Radhakrishnan, V., Shu, F. H., Somov, B. V., Sunyaev, R. A., Van Den Heuvel, E. P. J., Van Der Laan, H., and Ferraz-Mello, Sylvio

Abstract

The integration of the homological equation of the general perturbation theories of Chaps. 3 and 6 is only possible when the short-period frequencies $$ \nu _\mu ^* $$ (μ = 1..., M) obey the non-resonance condition 8.1$$ (h\nu *) = \sum\limits_{\mu = 1}^M {h_\mu } \nu _\mu ^* \ne 0 $$ for all h ≡ (h1..., hM) ∈ ZM appearing in the right-hand-side trigonometric polynomials. The strong restriction introduced by this condition is the very reason for which, in general, those theories cannot be extended to an arbitrarily high order. As discussed in Sect. 3.3.1, the set Dk ⊂ ZM of values of h grows with the order of approximation k and values of (hν*) smaller than any given limit may be formed as the set Dk grows. However, in the applications, we are often interested in a phase space domain where (hν*) = 0 for some h present in the given perturbation εR(θ, J; ε). We have, then, to extend canonical perturbation theories to such cases and learn how to construct formal solutions valid in the neighborhood of resonances. [ABSTRACT FROM AUTHOR]

Published
2007
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29. Single Resonance near a Singularity.

Author

Burton, W. B., Kuijpers, J. M. E., Bertola, F., Cassinelli, J. P., Cesarsky, C. J., Ehrenfreund, P., Engvold, O., Heck, A., Kaspi, V. M., Murdin, P. G., Pacini, F., Radhakrishnan, V., Shu, F. H., Somov, B. V., Sunyaev, R. A., Van Den Heuvel, E. P. J., Van Der Laan, H., and Ferraz-Mello, Sylvio

Abstract

The perturbation of a regular integrable Hamiltonian may lead to bifurcations in the phase portrait. Let us consider the case of only one resonance and the simple case of one degree of freedom. Let H0 be the Hamiltonian of a differential rotator: 9.1$$ H_0 = \frac{1} {2}\mathcal{V}_1^o (x_1^2 + y_1^2 ) + \frac{1} {8}\mathcal{V}_{11}^o (x_1^2 + y_1^2 )^2 $$ and let us assume that $$ \mathcal{V}_1^o $$ and $$ \mathcal{V}_{11}^o $$ have opposite signs, e.g. $$ \mathcal{V}_1^o < 0 $$ < 0 and $$ \mathcal{V}_{11}^o < 0 $$ > 0. In that case, H0 has a minimum on a circle of radius $$ \sqrt { - 4 - \nu _1^o /\nu _{11}^o } $$ on which the direction of motion changes. This is the classical case of a twist mapping and the Poincaré-Birkhoff theorem predicts that, when the rotator is perturbed, new centers and saddle points may appear in the phase portrait near the place where the frequency of the undisturbed rotator is zero (see [63]). [ABSTRACT FROM AUTHOR]

Published
2007
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30. Non-Singular Canonical Variables.

Author

Burton, W. B., Kuijpers, J. M. E., Bertola, F., Cassinelli, J. P., Cesarsky, C. J., Ehrenfreund, P., Engvold, O., Heck, A., Kaspi, V. M., Murdin, P. G., Pacini, F., Radhakrishnan, V., Shu, F. H., Somov, B. V., Sunyaev, R. A., Van Den Heuvel, E. P. J., Van Der Laan, H., and Ferraz-Mello, Sylvio

Abstract

The actions Ji defined by the phase integrals Ji = 1/2π ∮ pidqi may become singular. The simplest example is given by the actions of a Hamiltonian depending on the squares of the momenta. In this case, pi is proportional to $$ \dot q_i $$ and, as a consequence, the integral ⊂ pidqi is proportional to ⊂ $$ \int {\dot q_i^2 } dt $$ dt and, thus, sign definite. In other words, the integration path is always circulated in the same direction and the sign of Ji may not be reversed (Fig. 7.1). Consequently, the equations of motion in this variable are singular at Ji = 0. [ABSTRACT FROM AUTHOR]

Published
2007
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31. Lie Mappings.

Author

Burton, W. B., Kuijpers, J. M. E., Bertola, F., Cassinelli, J. P., Cesarsky, C. J., Ehrenfreund, P., Engvold, O., Heck, A., Kaspi, V. M., Murdin, P. G., Pacini, F., Radhakrishnan, V., Shu, F. H., Somov, B. V., Sunyaev, R. A., Van Den Heuvel, E. P. J., Van Der Laan, H., and Ferraz-Mello, Sylvio

Abstract

There is a straightforward way of introducing Lie series mappings into the study of Hamiltonian systems. Proposition 5.3.1 shows that the mapping defined by the series (5.25)-(5.26) is canonical and may be used in the construction of canonical perturbation theories. Thus, the reader interested only in such applications can go straight to those equations and skip the first two sections whose aim is to introduce Lie derivatives, Lie mappings and the relationship between Lie mappings and Jacobian canonical transformations. [ABSTRACT FROM AUTHOR]

Published
2007
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32. Lie Series Perturbation Theory.

Author

Burton, W. B., Kuijpers, J. M. E., Bertola, F., Cassinelli, J. P., Cesarsky, C. J., Ehrenfreund, P., Engvold, O., Heck, A., Kaspi, V. M., Murdin, P. G., Pacini, F., Radhakrishnan, V., Shu, F. H., Somov, B. V., Sunyaev, R. A., Van Den Heuvel, E. P. J., Van Der Laan, H., and Ferraz-Mello, Sylvio

Abstract

In 1966, the Poincaré and von Zeipel-Brouwer theories were rejuvenated by Hori [53] through the introduction of canonical transformations expressed by Lie series mappings instead of the classical Jacobian transformations. The use of mathematical operations in perturbation theories with the same properties as Lie derivatives and Lie series was already current among physicists [13] and, around 1960, in at least one instance (Sérsic [85]), it was suggested that Lie series could be used to represent the canonical transformations of Celestial Mechanics. [ABSTRACT FROM AUTHOR]

Published
2007
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33. Resonance.

Author

Burton, W. B., Kuijpers, J. M. E., Bertola, F., Cassinelli, J. P., Cesarsky, C. J., Ehrenfreund, P., Engvold, O., Heck, A., Kaspi, V. M., Murdin, P. G., Pacini, F., Radhakrishnan, V., Shu, F. H., Somov, B. V., Sunyaev, R. A., Van Den Heuvel, E. P. J., Van Der Laan, H., and Ferraz-Mello, Sylvio

Abstract

Delaunay was the first astronomer to use the mechanics of Hamilton and Jacobi to obtain the approximated solution of the equations of motion of a celestial body. His lunar theory [22] is a pioneer work in many respects. We credit Delaunay with the introduction of the set of angle-action variables ℓ, g, h, L, G, H in which the Lagrange equations for the variation of the orbital elements under a perturbation are canonical. His theory of the motion of the Moon is not a collection of clever tricks, as other theories in the old Celestial Mechanics. Having obtained the variation equations in canonical form, his problem was to find the solutions of the differential equations defined by the Hamiltonian 4.1$$ H = H_0 (J) + \varepsilon \sum\limits_{h \in D} {A_h } (J)cos(h\theta ), $$ where the canonical variables are J ≡ (J1..., JN) and θ ≡ (θ1..., θN), ε is a small parameter and D ⊂ ZN. The technique adopted by Delaunay is methodologically very clear. He defined an operation and performed it, successively, almost 500 times. This operation starts with the choice of one argument (h1θ) in (4.1) and the consideration of the dynamical system defined by the abridged Hamiltonian 4.2$$ \mathcal{F}_1 = H_0 (J) + \varepsilon A_{h_1 } (J)cos(h_1 \theta ). $$ This system is integrable, since the angles θi are present only through the linear combination (h1θ). [ABSTRACT FROM AUTHOR]

Published
2007
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34. Angle-Action Variables. Separable Systems.

Author

Burton, W. B., Kuijpers, J. M. E., Bertola, F., Cassinelli, J. P., Cesarsky, C. J., Ehrenfreund, P., Engvold, O., Heck, A., Kaspi, V. M., Murdin, P. G., Pacini, F., Radhakrishnan, V., Shu, F. H., Somov, B. V., Sunyaev, R. A., Van Den Heuvel, E. P. J., Van Der Laan, H., and Ferraz-Mello, Sylvio

Abstract

The trajectories of systems with one degree of freedom are the curves H(q1, p1) = E. As shown in Sect. 1.8, the equations of the motion are given by 2.1$$ t + \alpha _1 = q_1^* = \frac{{\partial S}} {{\partial E}}\mathop = \limits^{def} F_{11} (q_1 ), $$ where α1 is a constant and S = S(q1, E) is the solution of the Hamilton-Jacobi equation. [ABSTRACT FROM AUTHOR]

Published
2007
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35. Classical Perturbation Theories.

Author

Burton, W. B., Kuijpers, J. M. E., Bertola, F., Cassinelli, J. P., Cesarsky, C. J., Ehrenfreund, P., Engvold, O., Heck, A., Kaspi, V. M., Murdin, P. G., Pacini, F., Radhakrishnan, V., Shu, F. H., Somov, B. V., Sunyaev, R. A., Van Den Heuvel, E. P. J., Van Der Laan, H., and Ferraz-Mello, Sylvio

Abstract

Many general perturbation theories devised since the nineteenth century were founded on the powerful tools of Hamiltonian mechanics. They aimed at solving the specific problem of finding the solutions of the canonical system of 2N differential equations 3.1$$ \frac{{dq_i }} {{dt}} = \frac{{\partial H}} {{\partial p_i }}, \frac{{dp_i }} {{dt}} = - \frac{{\partial H}} {{\partial q_i }}, $$ (i = 1, 2..., N), where the Hamiltonian H is the energy of the system and may be written as 3.2$$ H = \mathcal{H}_0 (q,p) + \mathcal{R}(q,p,\varepsilon ) $$ with q ≡ (q1..., qN), p ≡ (p1..., pN). $$ \mathcal{H}_0 $$ is the Hamiltonian of a separable system and $$ \mathcal{R} $$ is a disturbing potential, analytical in some small parameter ε, and vanishing for ε = 0. [ABSTRACT FROM AUTHOR]

Published
2007
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36. The Hamilton-Jacobi Theory.

Author

Burton, W. B., Kuijpers, J. M. E., Bertola, F., Cassinelli, J. P., Cesarsky, C. J., Ehrenfreund, P., Engvold, O., Heck, A., Kaspi, V. M., Murdin, P. G., Pacini, F., Radhakrishnan, V., Shu, F. H., Somov, B. V., Sunyaev, R. A., Van Den Heuvel, E. P. J., Van Der Laan, H., and Ferraz-Mello, Sylvio

Abstract

Astronomers in the nineteenth century found that the form of the Lagrange-Laplace equations for the perturbed Keplerian motion becomes very simple when the set of variables known as Delaunay variables, 1.1$$ \begin{gathered} \ell = mean anomaly, L = \sqrt {\mu a} , \hfill \\ g = argument of the periapis, G = L\sqrt {1 - e^2 } , \hfill \\ h = longtitude of the node, H = G cos i, \hfill \\ \end{gathered} $$ is used (see [15]). Here, μ is the product of the gravitational constant and the mass of the central body, a the semi-major axis, e the orbital eccentricity and i the inclination of the orbit over the reference plane. [ABSTRACT FROM AUTHOR]

Published
2007
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38. Space Weather Research.

Author

Burton, W. B., Bertola, F., Cassinelli, J. P., Cesarsky, C. J., Ehrenfreund, P., Engvold, O., Heck, A., Van Den Heuvel, E. P. J., Kaspi, V. M., Kuijpers, J. M. E., Laan, H. van der, Murdin, P. G., Pacini, F., Radhakrishnan, V., Somov, B. V., Sunyaev, R. A., and Akasofu, Syun-Ichi

Published
2007
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39. Myth of the Emerging Flux Tubes: Sunspots and Solar Flares.

Author

Burton, W. B., Bertola, F., Cassinelli, J. P., Cesarsky, C. J., Ehrenfreund, P., Engvold, O., Heck, A., Van Den Heuvel, E. P. J., Kaspi, V. M., Kuijpers, J. M. E., Laan, H. van der, Murdin, P. G., Pacini, F., Radhakrishnan, V., Somov, B. V., Sunyaev, R. A., and Akasofu, Syun-Ichi

Published
2007
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40. Recurrent Geomagnetic Disturbances and the Solar Wind.

Author

Burton, W. B., Bertola, F., Cassinelli, J. P., Cesarsky, C. J., Ehrenfreund, P., Engvold, O., Heck, A., Van Den Heuvel, E. P. J., Kaspi, V. M., Kuijpers, J. M. E., Laan, H. van der, Murdin, P. G., Pacini, F., Radhakrishnan, V., Somov, B. V., Sunyaev, R. A., and Akasofu, Syun-Ichi

Published
2007
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42. Synthesis of Magnetospheric Substorm Phenomena.

Author

Burton, W. B., Bertola, F., Cassinelli, J. P., Cesarsky, C. J., Ehrenfreund, P., Engvold, O., Heck, A., Van Den Heuvel, E. P. J., Kaspi, V. M., Kuijpers, J. M. E., Laan, H. van der, Murdin, P. G., Pacini, F., Radhakrishnan, V., Somov, B. V., Sunyaev, R. A., and Akasofu, Syun-Ichi

Published
2007
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45. Search for the Unknown Quantity in the Solar Wind.

Author

Burton, W. B., Bertola, F., Cassinelli, J. P., Cesarsky, C. J., Ehrenfreund, P., Engvold, O., Heck, A., Van Den Heuvel, E. P. J., Kaspi, V. M., Kuijpers, J. M. E., Laan, H. van der, Murdin, P. G., Pacini, F., Radhakrishnan, V., Somov, B. V., Sunyaev, R. A., and Akasofu, Syun-Ichi

Published
2007
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46. Effects of Scintillations in GNSS Operation.

Author

Burton, W. B., Bertola, F., Cassinelli, J. P., Cesarsky, C. J., Ehrenfreund, P., Engvold, O., Heck, A., van Den Heuvel, E. P. J., Kaspi, V. M., Kuijpers, J. M. E., van Der Laan, H., Murdin, P. G., Pacini, F., Radhakrishnan, V., Somov, B. V., Sunyaev, R. A., Lilensten, Jean, Béniguel, Y., and Adam, J.-P.

Published
2007
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47. Finnish Experiences with Grid Effects of GIC's.

Author

Burton, W. B., Bertola, F., Cassinelli, J. P., Cesarsky, C. J., Ehrenfreund, P., Engvold, O., Heck, A., van Den Heuvel, E. P. J., Kaspi, V. M., Kuijpers, J. M. E., van Der Laan, H., Murdin, P. G., Pacini, F., Radhakrishnan, V., Somov, B. V., Sunyaev, R. A., Lilensten, Jean, and Elovaara, Jarmo

Published
2007
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48. Spatiotemporal Characteristics of the Ground Electromagnetic Field Fluctuations in the Auroral Region and Implications on the Predictability of Geomagnetically Induced Currents.

Author

Burton, W. B., Bertola, F., Cassinelli, J. P., Cesarsky, C. J., Ehrenfreund, P., Engvold, O., Heck, A., van Den Heuvel, E. P. J., Kaspi, V. M., Kuijpers, J. M. E., van Der Laan, H., Murdin, P. G., Pacini, F., Radhakrishnan, V., Somov, B. V., Sunyaev, R. A., Lilensten, Jean, and Pulkkinen, A.

Published
2007
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50. Geomagnetic Indices in Solar-Terrestrial Physics and Space Weather.

Author

Burton, W. B., Bertola, F., Cassinelli, J. P., Cesarsky, C. J., Ehrenfreund, P., Engvold, O., Heck, A., van Den Heuvel, E. P. J., Kaspi, V. M., Kuijpers, J. M. E., van Der Laan, H., Murdin, P. G., Pacini, F., Radhakrishnan, V., Somov, B. V., Sunyaev, R. A., Lilensten, Jean, Menvielle, M., and Marchaudon, A.

Abstract

Geomagnetic indices play a significant role in describing the magnetic configuration of the Earth's magnetosphere. In the past 15 years, they have become a key parameter in Space Weather research, being commonly used to detect and describe Space Weather events. Research is currently being carried out into using them for forecasting. The objective of this paper is to contribute to a better understanding of the usefulness, potential and limitations of geomagnetic indices in Space Weather research and applications [ABSTRACT FROM AUTHOR]

Published
2007
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