Unveiling the Influence of Dark Matter in Axially Symmetric Galaxies

We investigate the regular or chaotic nature of orbits of stars moving in the meridional plane (R,z) of an axially symmetric galactic model with a dense, massive spherical nucleus and a dark matter halo component. In particular, we study the influence of the fractional portion of the dark matter, by computing in each case the percentage of chaotic orbits, as well as the percentages of orbits of the main regular resonant families. In an attempt to distinguish between regular and chaotic motion, we use the fast Lyapunov indicator method to extensive samples of orbits obtained by integrating numerically the equations of motion as well as the variational equations. Furthermore, a technique which is based mainly on the field of spectral dynamics that utilises the Fourier transform of the time series of each coordinate is used for identifying the various families of regular orbits and also to recognise the secondary resonances that bifurcate from them. Two cases are studied in our work: (i) the case where we have a disk galaxy model and (ii) the case where our model represents an elliptical galaxy. A comparison with early related work is also made.

NUMERICAL AND EXPERIMENTAL STUDY OF REGULAR AND CHAOTIC MOTION OF TRIPLE PHYSICAL PENDULUM

Nonlinear dynamics of a real plane and periodically forced triple pendulum is investigated experimentally and numerically. Mathematical modeling includes details, taking into account some characteristic features (for example, real characteristics of joints built by the use of roller bearings) as well as some imperfections (asymmetry of the forcing) of the real system. Parameters of the model are obtained by a combination of the estimation from experimental data and direct measurements of the system's geometric and physical parameters. A few versions of the model of resistance in the joints are tested in the identification process. Good agreement between both numerical simulation results and experimental measurements have been obtained and presented. Some novel features of our real system chaotic dynamics have also been reported, and a novel approach of the rolling bearings friction modeling is proposed, among other.