[en] Published in summary form only

[en] The numbered asteroids are classified into families by a new method previously proposed by the author using the semi-major axis, the minimum value of the inclination and the argument of the perihelion as parameters, and the class characteristics are studied by several aspects. It seems to the author that there are two kinds of families, one being very compact in the phase space and containing many faint as well as a few bright asteroids and one being rather loose and bounded by secular and mean motion commensurable regions. (Auth.)

[en] Very simple arguments are used to show that some mathematically attractive viscous stresses, which prevent the formation of shocks and give a parabolic character to the equations of motion for continua in which they appear, are physically unacceptable because their material responses are affected by rigid motion.

[en] We present a geometric proof of Liouville's theorem on the existence of canonical coordinates for integrable systems. (Author)

No abstract available

[en] We introduce the Richelot class of superintegrable systems in N-dimensions whose n ≤ N equations of motion coincide with the Abel equations on the n - 1 genus hyperelliptic curve. Corresponding additional integrals of motion are the second-order polynomials of momenta and multiseparability of the Richelot superintegrable systems is related to the classical theory of covers of the hyperelliptic curves.

[en] The book consists of the Proceedings of the School on Qualitative Aspects and Applications of Nonlinear Evolution equations held at the ICTP Trieste between 10 September-5 October 1990. It includes Main Courses (5 lectures), Special Lectures (7 lectures) and Talks Given at the Seminars (13 lectures). A separate abstract was prepared for each lecture. Refs, figs and tabs

[en] The parametrically excited stability of a periodically stiffened beam under general periodic axial excitation is studied and the effect of periodic stiffeners on the beam stability is considered for the first time. The partial differential equation of motion of the beam with periodic stiffeners under axial excitation is given. The Galerkin method is used to convert the partial differential equation into ordinary differential equations with periodic time-varying parameters. The direct eigenvalue analysis method based on the Fourier expansion and generalized eigenvalue analysis is applied to solve the parametrically excited stability problem of the stiffened beam. A simply supported beam with periodic stiffeners under periodic axial excitation is considered for numerical investigation. The parametrically excited stability of the stiffened beam and the effects of stiffeners and excitation on the stability are illustrated by numerical results on unstable regions. (paper)

[en] The motion of a soliton in a supergravity background configuration is studied. The dynamics of the soliton is desribed by a trajectory in curved N = 2 superspace. For the proposed Langrangian the moments, the constraints and the generators of local supertranslations are displayed. An additional local gauge symmetry is exhibited. Special emphasis is laid on the classical equations of motion. These turn out to be a supersymmetric generalization of Papapetrou's equation of motion for a spinning particle in a gravitational field. (Author)

[en] We derive an exact equation of motion for a non-relativistic vortex in two- and three-dimensional models with a complex field. The velocity is given in terms of gradients of the complex field at the vortex position. We discuss the problem of reducing the field dynamics to a closed dynamical system with non-locally interacting strings as the fundamental degrees of freedom