Rotating saddle trap as Foucault's pendulum

One of the many surprising results found in the mechanics of rotating systems is the stabilization of a particle in a rapidly rotating planar saddle potential. Besides the counterintuitive stabilization, an unexpected precessional motion is observed. In this note we show that this precession is due to a Coriolis-like force caused by the rotation of the potential. To our knowledge this is the first example where such force arises in an inertial reference frame. We also propose an idea of a simple mechanical demonstration of this effect.Comment: 13 pages, 9 figure

Chaotic Phenomenon in Nonlinear Gyrotropic Medium

Nonlinear gyrotropic medium is a medium, whose natural optical activity depends on the intensity of the incident light wave. The Kuhn's model is used to study nonlinear gyrotropic medium with great success. The Kuhn's model presents itself a model of nonlinear coupled oscillators. This article is devoted to the study of the Kuhn's nonlinear model. In the first paragraph of the paper we study classical dynamics in case of weak as well as strong nonlinearity. In case of week nonlinearity we have obtained the analytical solutions, which are in good agreement with the numerical solutions. In case of strong nonlinearity we have determined the values of those parameters for which chaos is formed in the system under study. The second paragraph of the paper refers to the question of the Kuhn's model integrability. It is shown, that at the certain values of the interaction potential this model is exactly integrable and under certain conditions it is reduced to so-called universal Hamiltonian. The third paragraph of the paper is devoted to quantum-mechanical consideration. It shows the possibility of stochastic absorption of external field energy by nonlinear gyrotropic medium. The last forth paragraph of the paper is devoted to generalization of the Kuhn's model for infinite chain of interacting oscillators

Analysis of Transient Processes in a Radiophysical Flow System

Transient processes in a third-order radiophysical flow system are studied and a map of the transient process duration versus initial conditions is constructed and analyzed. The results are compared to the arrangement of submanifolds of the stable and unstable cycles in the Poincare section of the system studied.Comment: 3 pages, 2 figure

Discrete Nonholonomic LL Systems on Lie Groups

This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical nonholonomic systems, the Suslov top and the Chaplygin sleigh. The preservation of the reduced energy by the discrete flow is observed and the discrete momentum conservation is discussed.Comment: 32 pages, 13 figure

Conservation of energy and momenta in nonholonomic systems with affine constraints

We characterize the conditions for the conservation of the energy and of the components of the momentum maps of lifted actions, and of their `gauge-like' generalizations, in time-independent nonholonomic mechanical systems with affine constraints. These conditions involve geometrical and mechanical properties of the system, and are codified in the so-called reaction-annihilator distribution

Probability of local bifurcation type from a fixed point: A random matrix perspective

Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties as universal approximators (neural networks). The eigenvalue spectra is considered both numerically and analytically using previous work of Edelman et. al. Based upon the numerical evidence, various conjectures are presented. The conclusion is that in many circumstances, most bifurcations from fixed points of large dynamical systems will be due to complex eigenvalues. Nevertheless, surprising situations are presented for which the aforementioned conclusion is not general, e.g. real random matrices with Gaussian elements with a large positive mean and finite variance.Comment: 21 pages, 19 figure

Classical and Quantum Systems: Alternative Hamiltonian Descriptions

In complete analogy with the classical situation (which is briefly reviewed) it is possible to define bi-Hamiltonian descriptions for Quantum systems. We also analyze compatible Hermitian structures in full analogy with compatible Poisson structures.Comment: To appear on Theor. Math. Phy

Interaction of water vapour at 298 K with Al-MCM-41 materials synthesised at room temperature

Abstract The interaction of water vapour with Al-MCM-41, prepared by direct synthesis at ambient temperature and pressure, using tetraethoxysilane, aluminium sulfate, hexadecyltrimethylammonium bromide and ammonia, and its effect on the pore structure were studied in order to investigate the stability towards prolonged exposure to water vapour and the influence of the aluminium content. With this purpose two consecutive water adsorption isotherms were determined at 298 K on samples with Si/Al ratio between 15 and 100. The samples were characterised by X-ray diffraction and adsorption of nitrogen at 77 K and toluene at 298 K, prior to and after exposure to water vapour. Pore size distributions were calculated from nitrogen, toluene and water adsorption isotherms using, respectively, the NLDFT method, a recently developed hybrid MC-DBdB method and the DBdB macroscopic approximation. It was found that Al-MCM-41 samples are significantly stable and that the stability improves as the amount of aluminium increases. Upon prolonged exposure to water vapour, there is a small decrease in pore size (3-5%), pore volume (8-16%) and total surface area (3-7%). The structural changes are essentially a consequence of the surface hydroxylation that occurred and not a result of a partial collapse of the pore structure. Although the presence of some extraframework Al can contribute to the improvement of the stability by protecting the surface, it was concluded that tetracoordinated Al plays an important role. The stabilizing effect of the Al incorporated in the walls can result from a higher degree of condensation on the surface of the pore walls and from the mild acidity generated

Planar reorientation maneuvers of space multibody systems using internal controls

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77104/1/AIAA-11411-971.pd