The Motion of a Rigid Body in the Presence of a Gyrostatic : الحركات المغزلية السريعة لجسم متماسك في مجال قوة نيوتوني في حالة وجود العزم

In this study، the rotational motion of a rigid body about a fixed point in the Newtonian force field with a gyrostatic momentum about the z-axis is considered. The equations of motion and their first integrals are obtained and reduced to a quasi-linear autonomous system with two degrees of freedom with one first integral. Poincare's small parameter method is applied to investigate the analytical peri­odic solutions of the equations of motion of the body with one point fixed، rapidly spinning about one of the principal axes of the ellipsoid of inertia. A geometric interpretation of motion is given by using Euler's angles to describe the orientation of the body at any instant of time.

A Chaotic Three Dimensional Non-Linear Autonomous System Beyond Lorenz Type Systems

Some fundamental properties of a chaotic three-dimensional non-linear system of the Lorenz type systems were studied. The invariance, dissipation, bifurcation and the strange attractors were investigated and analyzed one 1-scroll, two 2-scroll and two 4-scroll attractors by adding control parameters to this system. The relationship and connecting function for the 2-scroll attractor of this system were also explored. DOI: http://dx.doi.org/10.3329/jbas.v36i2.12959 Journal of Bangladesh Academy of Sciences, Vol. 36, No. 2, 159-170, 2012

GENERATING 3-D SCROLL GRID ATTRACTORS OF FRACTIONAL DIFFERENTIAL SYSTEMS VIA STAIR FUNCTION

This paper discusses the stair function approach for the generation of scroll grid attractors of fractional differential systems. The one-directional (1-D) n-grid scroll, two-directional (2-D) (n × m)-grid scroll and three-directional (3-D) (n × m × l)-grid scroll attractors are created from a fractional linear autonomous system with a simple stair function controller. Being similar to the scroll grid attractors of classical differential systems, the scrolls of 1-D n-grid scroll, 2-D (n × m)-grid scroll and 3-D (n × m × l)-grid scroll attractors are located around the equilibria of fractional differential system on a line, on a plane or in 3D, respectively and the number of scrolls is equal to the corresponding number of equilibria.

DYNAMICS OF A SELF-GRAVITATING MAGNETIZED SOURCE

We consider a magnetized degenerate gas of fermions as the matter source of a homogeneous but anisotropic Bianchi I space–time with a Kasner-like metric. We examine the dynamics of this system by means of a qualitative and numerical study of Einstein–Maxwell field equations which reduce to a non-linear autonomous system. For all initial conditions and combinations of free parameters, the gas evolves from an initial anisotropic singularity into an asymptotic state that is completely determined by a stable attractor. Depending on the initial conditions the anisotropic singularity is of the "cigar" or "plate" types.

GENERATING CHAOS VIA A DYNAMICAL CONTROLLER

This Letter studies the generation of chaos from a linear autonomous system by employing a dynamical nonlinear feedback controller. The system setup is quite simple, and the only nonlinearity is a piecewise-quadratic function in the form of x|x|. Both computer simulation and circuit implementation are given to verify the chaos generated by this mechanism.