On one problem, associated with lateral oscillations of elastic-viscous-relaxating rod

We obtain the solution of the problem about lateral oscillations of elastic-viscous-relaxating rod of finite length, variable profile, and variable momentum of rotation inertia of rod elements about the axis that is perpendicular to oscillation plane.

Enigmatic Gravity Effects Observed during Solar Eclipses. Their Analyse by Quantum Model of Inertia and Gravitation

Foucault long pendulums, with spherical suspended mass, show Earth rotation by the constant velocity drift of their oscillation plane. Maurice Allais used a short, 84 centimeters pendulum, with a suspended bronze disc mass. He recorded its oscillation plane drift velocity, during solar eclipses, in 1954 and 1959. Both times, he noticed an anomalous drift of the oscillation plane. Several authors confirmed the effect, during next solar eclipses, with other types of pendulums. Then a group of Geophysicists, from the Science Academy of China, used an accurate digital gravimeter to measure Earth Gravity acceleration during March 09, 1997 solar eclipse. Their gravimeter recorded two drops of Earth Gravity acceleration (respectively 5.02 and 7.7 µ Gals) before and during first and last contacts of the Moon disc. However there was no acceleration drop during eclipse totality. Same phenomena were confirmed later, during next solar eclipses, with the same gravimeter. No classical causes for these facts were found, since modern gravimeters take care of temperature and atmospheric pressure variations. We analyse the effect of Moon rotation, and of solar Corona mass, in the frame of our Quantum model of Inertia and of Gravitation. The model predicts that Moon / Earth Gravity acceleration changes, when the Moon direction is close to the Sun one, as observed from the gravimeter place. That phenomenon should be tied to Quantum fluctuations dispersion by matter. Recorded measurements confirm that interpretation.

Numerical Study of the Elastic Pendulum on the Rotating Earth

The elastic pendulum is a simple physical system represented by nonlinear differential equations. Analytical solutions for the bob trajectories on the rotating earth may be obtained in two limiting cases: for the ideally elastic pendulum with zero unstressed string length and for the Foucault pendulum with an inextensible string. The precession period of the oscillation plane, as seen by the local observer on the rotating earth, is 24 hours in the first case and has a well-known latitude dependence in the second case. In the present work, we have obtained numerical solutions of the nonlinear equations for different string elasticities in order to study the transition from one precession period to the other. It is found that the transition is abrupt and that it occurs for a quite small perturbation of the ideally elastic pendulum, that is, for the unstressed string length equal to about 10−4 of the equilibrium length due to the weight of the bob.