Dzhanibekov effect in a physics classroom

The purpose of this publication is to present a novel approach to the demonstration of the Dzhanibekov effect. The main idea of our version is to use a lightweight spinning top of a spherical external form but distinct principal moments of inertia floating in the upward flow of air. As a result, the Dzhanibekov effect can be easily demonstrated anywhere on Earth: in any classroom, or even in the ‘home-lab’. The proposed demonstration allows one to observe the periodical flipping motion of the asymmetrical top with the clearly seen quasi-stable rotational phase. It may also become the base for various theoretical and experimental research projects for students.

MMX geodesy investigations: science requirements and observation strategy

In order to investigate the origin of Phobos and Deimos, the Japanese Martian Moons eXploration (MMX) mission is scheduled for launch in 2024. MMX will make comprehensive remote-sensing measurements of both moons and return regolith samples from Phobos to Earth. Geodetic measurements of gravity, shape, and rotation parameter of a body provides constraints on its internal structure reflecting its origin and evolution. Moments of inertia are important parameters to constrain the internal mass distribution, but they have not been well determined for the Martian moons yet. We discuss the mission requirements related to the moments of inertia to detect a potential heterogeneity of the mass distribution inside Phobos. We introduce mission instruments and operational strategies to meet the mission requirements. We present a preliminary imaging strategy from a quasi-satellite orbit for a base shape model that is expected to be created at the early stage of the mission. Geodetic products including ephemeris, gravity field, rotation parameter of Phobos, and spacecraft orbit are of importance not only for the geodetic study, but also for interpreting data from various mission instruments and selecting possible landing sites. Graphical Abstract

Study of Sexual Dimorphism in Metatarsal Bones: Geometric and Inertial Analysis of the Three-Dimensional Reconstructed Models

The aim of the present paper is to determine the sex of the individual using three-dimensional geometric and inertial analyses of metatarsal bones. Metatarsals of 60 adult Chinese subjects of both sexes were scanned using Aquilion One 320 Slice CT Scanner. The three-dimensional models of the metatarsals were reconstructed, and thereafter, a novel software using the center of mass set as the origin and the three principal axes of inertia was employed for model alignment. Eight geometric and inertial variables were assessed: the bone length, bone width, bone height, surface-area-to-volume ratio, bone density, and principal moments of inertia around the x, y, and z axes. Furthermore, the discriminant functions were established using stepwise discriminant function analysis. A cross-validation procedure was performed to evaluate the discriminant accuracy of functions. The results indicated that inertial variables exhibit significant sexual dimorphism, especially principal moments of inertia around the z axis. The highest dimorphic values were found in the surface-area-to-volume ratio, principal moments of inertia around the z axis, and bone height. The accuracy rate of the discriminant functions for sex determination ranged from 88.3% to 98.3% (88.3%–98.3% cross-validated). The highest accuracy of function was established based on the third metatarsal bone. This study showed for the first time that the principal moment of inertia of the human bone may be successfully implemented for sex estimation. In conclusion, the sex of the individual can be accurately estimated using a combination of geometric and inertial variables of the metatarsal bones. The accuracy should be further confirmed in a larger sample size and be tested or independently developed for distinct population/age groups before the functions are widely applied in unidentified skeletons in forensic and bioarcheological contexts.

Technics for experimental determination of CubeSat mass-centering and inertial characteristics

Due to inability to set a high accuracy of initial data in theoretical calculations of mass-centering and inertial characteristics of nanosatellites, a problem arises concerning the experimental determination of their actual values. For a number of reasons, the devices designed for large spacecraft are not appropriate for small ones. This paper describes a device for measuring the center of mass coordinates and moments of inertia developed at Samara University specifically for CubeSat nanosatellites, as well as a technology for experimental determination of the design parameters of nanoclass spacecraft. The accuracy of determining the design parameters using the proposed device is confirmed by a series of experiments with standards. Key words: nanosatellite, center of mass coordinates, moment of inertia, inertia tensor, measuring platform.

Modern Walking Robots: A Brief Overview

In this review, we would like to present some of the most interesting modern designs of walking robots: bipedal, quadropedal, hexopedal, and octopods. Their advantages and disadvantages are highlighted. It has been determined that structures with eight or more limbs are ineffective due to high level of electricity consumption. The use of more than six number of legs does not give noticeable advantages in profile cross-country ability or maneuverability, however, it allows to reduce the forces and moments of inertia forces due to decrease in mode coefficient (ratio of time spent by propulsor in support to time of entire step), and, consequently, smoother leg movements in swing phase.

Rotational Diode: Clockwise/Counterclockwise Asymmetry in Conducting and Mechanical Properties of Rotating (semi)Conductors

It is difficult to imagine an isolated classical object which possess different moments of inertia when it is uniformly rotated about the same axis with the same angular frequency in opposite, clockwise and counterclockwise, directions. We argue that due to quantum effects, certain (semi-) conductors should exhibit asymmetry in their mechanical and conducting properties with respect to the opposite rotations. We show that a cylinder made of a suitably chosen semiconductor, coated in a metallic film and placed in the magnetic-field background, can serve as a “rotational diode”, which conducts electricity only at a specific range of angular frequencies. The critical angular frequency and the direction of rotation can be tuned with the magnetic field’s strength. Mechanically, the rotational diode possesses different moments of inertia when rotated in clockwise and counterclockwise directions. These effects emerge as a particularity of the Fermi-Dirac statistics of electrons in rotating conductors.

Controlled Change in the Dimensions of an Axisymmetric Spacecraft Descending in the Atmosphere of Mars

In the presented work, a controlled change by dimensions of a spacecraft descending in the atmosphere of Mars is considered. The aim of the work is to obtain a method for calculating the mass and mass-geometric characteristics of a spacecraft when changing its dimensions, which provides angular velocity passive control during the descent of this spacecraft in a low-density atmosphere. In the process of solving this problem, the geometric and mass-geometric characteristics of the descent spacecraft (volume, cross-sectional area, moments of inertia) were calculated. It is assumed that the outer shape of the spacecraft posterior to the incoming flow is a one-sheet rotational hyperboloid, which changes its dimensions during the spacecraft descent in the low-density atmosphere of Mars. As a result of solving the nonlinear programming problem, the minimum and maximum values of the main axial moments of inertia are obtained, which able to spin the spacecraft relative to the longitudinal axis of symmetry. The initial data for solving the nonlinear programming problem are the minimum volume and the maximum cross-sectional area of the hyperboloid, calculated according to the specified intervals of the variable controlling the dimensions of this surface. The method for calculating the mass and mass-geometric characteristics of a spacecraft when changing its dimensions ispresented, which makes it possible to control the magnitude of the angular velocity of a symmetric spacecraft in the low-density atmosphere of Mars without the use of onboard jet engines. In particular, it is shown in the work that as the height of the hyperboloid increases, the moment of inertia about the spacecraft longitudinal axis of symmetry decreases, accompanied by an increase in the moments of inertia about the transverse axes of symmetry. It can be shown that in this case there is an increase in the angular velocity of the spacecraft about the longitudinal axis, which makes it possible to achieve a stable orientation of the spacecraft upon entering the atmosphere. However, a more detailed study of the dynamics ofthe spacecraft relative motionwith a changeable shape in the atmosphere is beyond the scope of this work, but it can be presented in further publications.