The Stability of Certain Motion of a Charged Gyrostat in Newtonian Force Field

This work aims to study the stability of certain motions of a rigid body rotating about its fixed point and carrying a rotor that rotates with constant angular velocity about an axis parallel to one of the principal axes. This motion is presumed to take place due to the combined influence of the magnetic field and the Newtonian force field. The equations of motion are deduced, and moreover, they are expressed as a Lie–Poisson Hamilton system. The permanent rotations are calculated and interpreted mechanically. The sufficient conditions for instability are presented employing the linear approximation method. The energy-Casimir method is applied to gain sufficient conditions for stability. The regions of linear stability and Lyapunov stability are illustrated graphically for certain values of the parameters.

Casimir and non-Newtonian force experiment (CANNEX): Review, status, and outlook

Many theoretical approaches aiming to explain dark matter or dark energy predict variations of Newton’s law of gravity at sub-millimeter separations. In this low-energy domain, force metrology provides an alternative to astronomical observations and high-energy experiments in the search for new physics. The Casimir And Non-Newtonian force EXperiment (CANNEX) has been designed from the ground up to allow for metrological force measurements between truly parallel macroscopic flat plates in the separation range 3–30 micrometer. Benefiting from this geometry, the experiment could potentially reach sensitivities of [Formula: see text]nN/m2 for pressures and [Formula: see text]mN/m3 for pressure gradients. Achieving such precision would enable us to test a variety of non-Newtonian interactions and to unambiguously detect thermal Casimir forces at large separation. In this paper, we review the experimental setup together with proposed improvements, and give an outlook on potential measurements that will be performed once the setup has been rebuilt at its new location in Vienna.

Rebuttal to : ‘The formulation of dynamic Newtonian advanced gravity, DNAg’

In this short note we rebut the claims made by Andrew Worsley. The author claims that “the equations for gravity can be adapted by defining the equations for the curvature of space–time in terms of geodesics. Using these equations, we translate this curvature back into equations for an advanced Newtonian force of gravity.” when, in reality he simply generates an ansatz that is falsified by existent experiments, experiments that the author is unaware of.

On the motion of a gyro in the presence of a Newtonian force field and applied moments

This work focuses on the motion of a dynamical model that consists of a symmetric rigid body (gyro) that rotates about a fixed point similar to Lagrange’s gyroscope. This body is acted upon by external forces represented by a Newtonian force field, gyro torques about the principal axes of inertia of the gyro and perturbing moments acting on the same axes. Assuming that, the gyro initially has a high angular velocity about the dynamic axis of symmetry. The averaging technique is used to obtain a more appropriate averaging system for the governing system of equations of motion in terms of a small parameter. Therefore, the analytical solutions of this system for two applications, depending on different forms of perturbing moments, are presented. These solutions are represented graphically to clarify the effectiveness of the different parameters of the body on the motion.

On the dynamical motion of a gyro in the presence of external forces

This work shed light on the motion of a symmetric rigid body (gyro) about one of its principal axes in the presence of a Newtonian force field besides a gyro moment in which its second component equals null. It is assumed that the body center of mass is shifted slightly relative to the dynamic symmetry axis. The governing equations of motion are investigated taking into account some initial conditions. The desired solutions of these equations are achieved in framework of the small parameter method. The periodic solutions for the case of irrational frequencies are investigated. Euler’s angles have been used to interpret the motion at any time. The geometrical representations of the obtained solutions and the phase plane schemas of these solutions are announced during several plots. Discussion of the results is presented to reinforce the importance of the considered gyro moment and the Newtonian force field. The significance of this problem is due to the framework of its several applications in different industries such as airplanes, submarines, compasses, spaceships, and guided missiles.

On Permanent Rotations of a System of Two Coupled Gyrostats in a Central Newtonian Force Field

This paper studies the problem of the motion of a chain of two gyrostats coupled by an ideal spherical joint. The chain moves about a fixed point in a central Newtonian force field. Under the assumption that the gyrostatic moment of each gyrostat is constant relative to its carrier, the paper establishes and analyzes the conditions for existence of the chain’s permanent rotations about a vertical axis. For a case when each gyrostat has the mass distribution analogous to the one of a Lagrange gyroscope, the paper derives and analyzes the necessary conditions for stability of the permanent rotations. The findings of the paper extend corresponding results in the dynamics of a single gyrostat to a case of the multibody chain as well as generalize some of the known properties of permanent rotations in the many-body dynamics.