arXiv subjects
Publications and source records attributed to A. L. Salas-Brito.
We apply the Ott, Grebogy and Yorke mechanism for the control of chaos to the analytical oscillator model of a leaky tap obtaining good results. We exhibit the robustness of the control against both dynamical noise and measurement noise.A possible way of controlling experimentally a leaky tap using magnetic-field-produced variations in the viscosity of a magnetorheological fluid is suggested.
The hodograph, i.e. the path traced by a body in velocity space, was introduced by Hamilton in 1846 as an alternative for studying certain dynamical problems. The hodograph of the Kepler problem was then investigated and shown to be a circle, it was next used to investigate some other properties of the motion. We here propose a new method for tracing the hodograph and the corresponding configuration space orbit in Kepler's problem starting from the initial conditions given and trying to use no more than the methods of synthetic geometry in a sort of Newtonian approach. All of our geometric constructions require straight edge and compass only.
The hodograph of the Kepler-Coulomb problem, that is, the path traced by its velocity vector, is shown to be a circle and then it is used to investigate other properties of the motion. We obtain the configuration space orbits of the problem starting from initial conditions given using nothing more than the methods of synthetic geometry so close to Newton's approach. The method works with elliptic, parabolic and hyperbolic orbits; it can even be used to derive Rutherford's relation from which the scattering cross section can be easily evaluated. We think our discussion is both interesting and useful inasmuch as it serves to relate the initial conditions with the corresponding trajectories in a purely geometrical way uncovering in the process some seldom discussed interesting connections.
A novel realization of the classical SU(2) algebra is introduced for the Dirac relativistic hydrogen atom defining a set of operators that, besides, allow the factorization of the problem. An extra phase is needed as a new variable in order to define the algebra. We take advantage of the operators to solve the Dirac equation using algebraic methods. To acomplish this, a similar path to the one used in the angular momentum case is employed; hence, the radial eigenfuntions calculated comprise non unitary representations of the algebra. One of the interesting properties of such non unitary representations is that they are not labeled by integer nor by half-integer numbers as happens in the usual angular momentum representation.
The superposition principle is a very basic ingredient of quantum theory. What may come as a surprise to many students, and even to many practitioners of the quantum craft, is tha superposition has limitations imposed by certain requirements of the theory. The discussion of such limitations arising from the so-called superselection rules is the main purpose of this paper. Some of their principal consequences are also discussed. The univalence, mass and particle number superselection rules of non-relativistic quantum mechanics are also derived using rather simple methods.