Theorem on the proportionality of inertial and gravitational masses in classical mechanics

We considered the problem of the proportionality of inertial and gravitational masses in classical mechanics. We found that the kinetic energy of a material mass point m in a circular motion with a constant angular velocity around another material point M depends only on its gravitational mass. This fact, together with the known result that the straight line is a circumference with an infinite radius, allowed us to prove the proportionality between the inertial and gravitational masses.Comment: ReVTeX file, 10p

On the Machian Origin of Inertia

We examine Sciama's inertia theory: we generalise it, by combining rotation and expansion in one unique model, we find the angular speed of the Universe, and we stress that the theory is zero-total-energy valued. We compare with other theories of the same null energy background. We determine the numerical value of a constant which appears in the Machian inertial force expression devised by Graneau and Graneau[2], by introducing the above angular speed. We point out that this last theory is not restricted to Newtonian physics as those authors stated but is, in fact, compatible with other cosmological and gravitational theories. An argument by Berry[7] is shown in order to "derive" Brans-Dicke relation in the present context.Comment: 10 pages including front one. New version was accepted to publication by Astrophysics and Space Scienc

Weber-like interactions and energy conservation

Velocity dependent forces varying as $k(\hat{r}/r)(1 - \mu \dot{r}^2 + \gamma r \ddot{r})$ (such as Weber force), here called Weber-like forces, are examined from the point of view of energy conservation and it is proved that they are conservative if and only if $\gamma=2\mu$. As a consequence, it is shown that gravitational theories employing Weber-like forces cannot be conservative and also yield both the precession of the perihelion of Mercury as well as the gravitational deflection of light.Comment: latex, 11 pages, no figure

MIDOT: A novel probe for monitoring high-current flat transmission lines

This paper was published in the journal Review of Scientific Instruments and the definitive published version is available at http://dx.doi.org/10.1063/1.4971246A novel inductive probe, termed MIDOT, was developed for monitoring high-current flat transmission lines. While being inexpensive the probe does not require calibration, is resistant to both shock waves and temperature variations, and it is easy to manufacture and mount. It generates strong output signals that are relatively easy to interpret and has a detection region limited to a pre-defined part of the transmission line. The theoretical background related to the MIDOT probes, together with their practical implementation in both preliminary experimentation and high-current tests, is also presented in the paper. The novel probe can be used to benchmark existing 2D numerical codes used in calculating the current distribution inside the conductors of a transmission line but can easily detect an early movement of a transmission line component. The probe can also find other applications, such as locating the position of a pulsed current flowing through a thin wire