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Register a new userSwinging Atwoods Machine: Experimental and Theoretical Studies
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Jacques-Arthur Weil Dr
Publication date
2009
fields
Physics
and research's language is
English
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A Swinging Atwood Machine (SAM) is built and some experimental results concerning its dynamic behaviour are presented. Experiments clearly show that pulleys play a role in the motion of the pendulum, since they can rotate and have non-negligible radii and masses. Equations of motion must therefore take into account the inertial momentum of the pulleys, as well as the winding of the rope around them. Their influence is compared to previous studies. A preliminary discussion of the role of dissipation is included. The theoretical behaviour of the system with pulleys is illustrated numerically, and the relevance of different parameters is highlighted. Finally, the integrability of the dynamic system is studied, the main result being that the Machine with pulleys is non-integrable. The status of the results on integrability of the pulley-less Machine is also recalled.
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We study the Kowalevski expansions near singularities of the swinging Atwoods machine. We show that there is a infinite number of mass ratios $M/m$ where such expansions exist with the maximal number of arbitrary constants. These expansions are of the so--called weak Painleve type. However, in view of these expansions, it is not possible to distinguish between integrable and non integrable cases.
In this study we describe lab experiments on determining the above water reflectance Rrs coefficient, and the water attenuation coefficient Kd for fresh water. Different types of screens (totally absorbent, gray, etc.) were submerged in water (0-0.6 m) and illuminated from outside. The spectral density of the water leaving radiance was measured for different depths. The results were ran by a code which took into account the geometry of the incident irradiation, the geometry of the screen under water, and boundary conditions at the water surface provided by the radiation transfer theory. From the experimental data and our model we obtain the spectral distribution of the attenuation coefficient for fresh water and compared it with other data in literature. These experiments, performed in the Nonlinear Wave Lab at ERAU# represent just a preliminary calibration of the experimental protocol. More tests with water of different degrees of turbidity, and possibly wave filed at the water surface are in progress and will be presented in a forthcoming paper.
Molecules containing superheavy atoms can be artificially created to serve as sensitive probes for study of symmetry-violating phenomena. Here, we provide a detailed theoretical study for diatomic molecules containing the superheavy lawrencium nuclei. The sensitivity to time-reversal violating properties was studied for different neutral and ionic molecules. The effective electric fields in these systems were found to be about 3-4 times larger than other known molecules on which electron electric dipole moment experiments are being performed. Similarly, these superheavy molecules exhibit an enhancement of more than 5 times for parity- and time-reversal-violating scalar-pseudoscalar nucleus-electron interactions. We also briefly comment on some experimental aspects by discussing the production of these systems.
The dynamics of a spherical body with a non-uniform mass distribution rolling on a plane were discussed by Sergey Chaplygin, whose 150th anniversary we celebrate this year. The Chaplygin top is a non-integrable system, with a colourful range of interesting motions. A special case of this system was studied by Edward Routh, who showed that it is integrable. The Routh sphere has centre of mass offset from the geometric centre, but it has an axis of symmetry through both these points, and equal moments of inertia about all axes orthogonal to the symmetry axis. There are three constants of motion: the total energy and two quantities involving the angular momenta. It is straightforward to demonstrate that these quantities, known as the Jellett and Routh constants, are integrals of the motion. However, their physical significance has not been fully understood. In this paper, we show how the integrals of the Routh sphere arise from Emmy Noethers invariance identity. We derive expressions for the infinitesimal symmetry transformations associated with these constants. We find the finite version of these symmetries and provide their geometrical interpretation. As a further demonstration of the power and utility of this method, we find the Noether symmetries and corresponding Noether integrals for a system introduced recently: the Chaplygin ball on a rotating turntable, confirming that the known integrals are directly obtained from Noethers theorem.
X-ray diffraction (XRD) and Mossbauer spectroscopy techniques combined with theoretical calculations based on the Korringa-Kohn-Rostoker (KKR) electronic structure calculation method were used to investigate sigma-phase Fe_{100-x}Re_{x} alloys (x = 43, 45, 47, 49 and 53). Structural data such as site occupancies and lattice constants were derived from the XRD patters, while the average isomer shift and distribution curves of the quadrupole splitting were obtained from the Mossbauer spectra. Fe-site charge-densities and the quadrupole splittings were computed with the KKR method for each lattice site. The calculated quantities combined with the experimentally determined site occupancies were successfully used to decompose the measured Mossbauer spectra into five components corresponding to the five sublattices.
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