Grazing Orbit Research Articles

Grazing Orbits and Related Local Bifurcations of an Oscillator with Continuous and Piecewise-Linear Restoring Force

One critical case for the motion of a periodically excited oscillator with continuous and piecewise-linear restoring force is that the motion happens to graze a switching plane between two linear regions of the restoring force. This article presents a numerical scheme for locating the periodic grazing orbit first. Then, through a brief analysis, the article shows that the grazing phenomenon turns the stability trend of the periodic orbit so abruptly that it may be impossible to predict an incident local bifurcation with the variation of a control parameter from the concept of smooth dynamic systems. The numerical simulation in the article well supports the scheme and the analysis, and shows an abundance of grazing phenomena in an engineering range of the excitation frequency.

DETECTION OF GRAZING ORBITS AND INCIDENT BIFURCATIONS OF A FORCED CONTINUOUS, PIECEWISE-LINEAR OSCILLATOR

A critical phenomenon in a continuous, piecewise-linear oscillator subjected to periodic excitation is considered, in which a periodic orbit happens to graze a switching plane between two linear regions of the oscillator at zero velocity. The analysis shows that if the piecewise linearity of the oscillator changes dramatically on the switching plane, the phenomenon turns the stability trend of the periodic orbit so abruptly that it may be hard to predict an incident bifurcation, although it is of a local type, according to the concepts of smooth dynamical systems. To detect the critical phenomenon induced by the non-smooth nature of the oscillator, a numerical scheme of searching for all periodic grazing orbits is presented, as well as a test function for grazing phenomena in tracing a branch of a periodic orbit. There follows a numerical simulation based on the scheme and the test function, which reveals an abundance of grazing phenomena and incident bifurcations of the oscillator.

Resonance atEc.m.=12.8MeV in theC12+O16system

An intermediate-type resonance of width GAMMA/sub c. m./ = 130+-25 keV has been observed in the excitation functions of the n, p, d, and ..cap alpha..-particle exit channels at E/sub c. m./ = 12.77 MeV in the /sup 12/C + /sup 16/O reaction. The energy of the resonance as well as its probable spin J = 8h-bar in good agreement with the predictions obtained from the semiclassical expression for the grazing orbit.

The role of savanna in nomadic pastoralism: some observations from western Bornu, Nigeria.

The vegetation of W. Bornu in N. Nigeria, its environment, physiognomy and flora are described. The savannah has developed under the combined influence of a severe dry season, shifting cultivation, grazing and the resulting annual fires. The savannah constitutes the grazing orbit of nomadic pastoralists who have adapted their system of cattle husbandry to the seasonal variation of the grazing land by a cyclic transhumance pattern of their families and herds. A. (Abstract retrieved from CAB Abstracts by CABI’s permission)