TRANSLATIONAL-ROTATIONAL MOTION OF THE TRIAXIAL BODY WITH VARIABLE COMPRESSIONS IN THE PRESENCE OF REACTIVE FORCES AND MOMENTS

2020 ◽  
Vol 69 (1) ◽  
pp. 241-246
Author(s):  
M.Zh. Minglibayev ◽  
◽  
O.B. Baisbayeva ◽  
Keyword(s):  
Coordinate System ◽  
Rotational Motion ◽  
Variable Mass ◽  
Spherical Body ◽  
Relative Orientation ◽  
The Body ◽  
Variable Size ◽  
Osculating Elements ◽  
Dynamic Shape ◽  
Central Gravitational Field

In this paper we investigated the translational-rotational motion of a triaxial body of constant dynamic shape and variable mass and size in a non-stationary Newtonian central gravitational field. Differential equations of the translationalrotational motion of the triaxial non-stationary body in the relative coordinate system with the origin at the center of a non-stationary spherical body are derived. The axes of the own coordinate system of the non-stationary triaxial body are directed along the principle axes of inertia of the body and we assumed that in the course of evolution their relative orientation remains unchanged. An analytical expression for the force function of the Newtonian interaction of the triaxial body of variable mass and size with a spherical body of variable size and mass is given. In the presence of reactive forces and moments the equations of translational-rotational motion of a triaxial non-stationary body in osculating elements are obtained in the presence of reactive forces and moments.

scholarly journals INVESTIGATION OF THE EVOLUTION EQUATIONS OF THE AXISYMMETRIC BODY WITH

2020 ◽  
Vol 69 (1) ◽  
pp. 247-252
Author(s):  
M.Zh. Minglibayev ◽  
◽  
S.B. Bizhanova ◽  
Keyword(s):  
Coordinate System ◽  
Rotational Motion ◽  
Evolution Equations ◽  
Second Harmonic ◽  
Variable Mass ◽  
Dynamic Structure ◽  
Approximate Expression ◽  
Axisymmetric Body ◽  
Osculating Elements ◽  
Two Bodies

In this article we consider mutually gravitating non-stationary two bodies: first body is «central», it is a sphere with a spherical density distribution, the second body is «satellite», which has an axisymmetric dynamic structure and form. Newtonian force interaction is characterized by an approximate expression of the force function, which takes into account the second harmonic. The differential equation of translational-rotational motion of the axisymmetric body is derived with variable mass and variable size in a relative coordinate system. The axes of the own coordinate system for nonstationary two bodies coincides with the main axes of inertia and this position remains unchanged during evolution. The mass of bodies are varied isotropically in the different rates. The problem is investigated by methods perturbation theory. The equations of secular perturbations of translational-rotational motion of satellite are deduced in the analogues osculating elements Delaunay-Andoyer. The solutions of the differential equations of the perturbed motion are obtained by the numerical method and the graphs are constructed using the Wolfram Mathematica package.

On the motion of bodies based on changes in the kinetic moment

2019 ◽  
Vol 20 (4) ◽  
pp. 267-275
Author(s):  
Yury N. Razoumny ◽  
Sergei A. Kupreev
Keyword(s):  
Center Of Mass ◽  
Stellar Dynamics ◽  
Elementary Particles ◽  
The Body ◽  
Accelerated Motion ◽  
Indirect Confirmation ◽  
Physical Principles ◽  
Two Bodies ◽  
Central Gravitational Field ◽  
Kinetic Moment

The controlled motion of a body in a central gravitational field without mass flow is considered. The possibility of moving the body in the radial direction from the center of attraction due to changes in the kinetic moment relative to the center of mass of the body is shown. A scheme for moving the body using a system of flywheels located in the same plane in near-circular orbits with different heights is proposed. The use of the spin of elementary particles is considered as flywheels. It is proved that using the spin of elementary particles with a Compton wavelength exceeding the distance to the attracting center is energetically more profitable than using the momentum of these particles to move the body. The calculation of motion using hypothetical particles (gravitons) is presented. A hypothesis has been put forward about the radiation of bodies during accelerated motion, which finds indirect confirmation in stellar dynamics and in an experiment with the fall of two bodies in a vacuum. The results can be used in experiments to search for elementary particles with low energy, explain cosmic phenomena and to develop transport objects on new physical principles.

scholarly journals Zur exakten Behandlung von kollektiven Rotationen Teil A: Theorie / On the Exact Treatment of Collective Rotations Part A: Theory

1973 ◽  
Vol 28 (2) ◽  
pp. 206-215
Author(s):  
Hanns Ruder
Keyword(s):  
Coordinate System ◽  
Perturbation Expansion ◽  
Rotational Energy ◽  
The Body ◽  
System A ◽  
N Body Problem ◽  
Definition Of ◽  
Fixed System ◽  
Body Fixed Coordinate System ◽  
Groundstate Energy

Basic in the treatment of collective rotations is the definition of a body-fixed coordinate system. A kinematical method is derived to obtain the Hamiltonian of a n-body problem for a given definition of the body-fixed system. From this exact Hamiltonian, a consequent perturbation expansion in terms of the total angular momentum leads to two exact expressions: one for the collective rotational energy which has to be added to the groundstate energy in this order of perturbation and a second one for the effective inertia tensor in the groundstate. The discussion of these results leads to two criteria how to define the best body-fixed coordinate system, namely a differential equation and a variational principle. The equivalence of both is shown.

Contact force analysis on two-fingered robot grasping

2020 ◽  
pp. 146441932096402
Author(s):  
Jiun-Ru Chen ◽  
Wei-En Chen ◽  
CH Liu ◽  
Yin-Tien Wang ◽  
CB Lin ◽  
...  
Keyword(s):  
Kinetic Analysis ◽  
Contact Force ◽  
Numerical Procedure ◽  
Spherical Body ◽  
Solution Procedure ◽  
The Body ◽  
Contact Forces ◽  
Grasping Forces ◽  
Robot Grasping ◽  
Force Displacement

A procedure for inverse kinetic analysis on two hard fingers grasping a hard sphere is proposed in this study. Contact forces may be found for given linear and angular accelerations of a spherical body. Elastic force-displacement relations predicted by Hertz contact theory are used to remove the indeterminancy produced by rigid body modelling. Two types of inverse kinetic analysis may be dealt with. Firstly, as the fingers impose a given tightening displacement on the body, and carry it to move with known accelerations, corresponding grasping forces may be determined by a numerical procedure. In this procedure one contact force may be chosen as the principal unknown, and all other contact forces are expressed in terms of this force. The numerical procedure is hence very efficient since it deals with a problem with only one unknown. The solution procedure eliminates slipping thus only nonslip solutions, if they exist, are found. Secondly, when the body is moving with known accelerations, if the grasping direction of the two fingers is also known, then the minimum tightening displacement required for non-sliding grasping may be obtained in closed form. In short, the proposed technique deals with a grasping system that has accelerations, and in this study the authors show that indeterminancy may be used to reduce the complexity of the problem.

On planar oscillations of a body with a variable mass distribution in an elliptic orbit

2011 ◽  
Vol 225 (10) ◽  
pp. 2288-2295 ◽  
Author(s):  
A Burov ◽  
I Kosenko
Keyword(s):  
Mass Distribution ◽  
Large Scale ◽  
Variable Mass ◽  
Relative Equilibria ◽  
The Body ◽  
Global Dynamics ◽  
Central Field ◽  
Attitude Dynamics ◽  
Orbital Eccentricity ◽  
Space Elevators

Planar motion of an orbiting body having a variable mass distribution in a central field of gravity is under analysis. Within the so-called ‘satellite approximation’ planar attitude dynamics is reduced to the 3/2-degrees of freedom description by one ODE of second order. The law of the mass distribution variations implying an existence of the special relative equilibria, such that the body is oriented pointing to the attracting centre by the same axis for any value of the orbit eccentricity is indicated. For particular example of an orbiting dumb-bell equipped by a massive cabin, wandering between the ends of the dumb-bell. For this example stability of the equilibria such that the dumb-bell ‘points to’ the attracting centre by one of its ends is studied. The chaoticity of global dynamics is investigated. Two important examples of a vibrating dumb-bell and of a dumb-bell equipped by a cabin wandering between its endpoints are considered. The dynamics of space objects, including moving elements, has been investigated by many authors. These studies usually have been connected with the necessity to estimate the influence of relative motions of moving parts, for example, crew motions [ 1 , 2 ], circulation of liquids [ 3 ], etc. on the attitude dynamics of a spacecraft. The development of projects of large-scale space systems with mobile elements, in particular, of satellite systems with tethered elements and space elevators, has posed problems related to their dynamics. Various aspects of the role of mass distribution even for the simplest orbiting systems, like dumb-bell systems are known since the publications [ 4 – 7 ], etc. The possibility of the sudden loss of stability because of the mass redistribution has been pointed out in reference [ 8 ] (see also references [ 9 – 13 ]). The considered system belongs to the mentioned class of systems and represents by itself one of the simplest systems allowing both analytical and numerical treatment, without supplementary simplifying assumptions such as smallness of the orbital eccentricity. Another set of applied problems is related to orientation keeping of the system for deployment and retrieval of tethered subsatellites as well as for relative cabin motions of space elevators. In particular, the problem of the stabilization/destabilization possibility for the given state of motion due to rapid oscillations of the cabin exists. This could be the subject of another additional investigation.

scholarly journals Computation of electrostatic fields in anisotropic human tissues using the Finite Integration Technique (FIT)

2005 ◽  
Vol 2 ◽  
pp. 309-313 ◽  
Author(s):  
V. C. Motresc ◽  
U. van Rienen
Keyword(s):  
Coordinate System ◽  
Electromagnetic Fields ◽  
Human Body ◽  
Local Coordinate System ◽  
Anisotropic Materials ◽  
The Body ◽  
Integration Technique ◽  
Data Set ◽  
Computer Data ◽  
Finite Integration Technique

Abstract. The exposure of human body to electromagnetic fields has in the recent years become a matter of great interest for scientists working in the area of biology and biomedicine. Due to the difficulty of performing measurements, accurate models of the human body, in the form of a computer data set, are used for computations of the fields inside the body by employing numerical methods such as the method used for our calculations, namely the Finite Integration Technique (FIT). A fact that has to be taken into account when computing electromagnetic fields in the human body is that some tissue classes, i.e. cardiac and skeletal muscles, have higher electrical conductivity and permittivity along fibers rather than across them. This property leads to diagonal conductivity and permittivity tensors only when expressing them in a local coordinate system while in a global coordinate system they become full tensors. The Finite Integration Technique (FIT) in its classical form can handle diagonally anisotropic materials quite effectively but it needed an extension for handling fully anisotropic materials. New electric voltages were placed on the grid and a new averaging method of conductivity and permittivity on the grid was found. In this paper, we present results from electrostatic computations performed with the extended version of FIT for fully anisotropic materials.

scholarly journals How visual experience and task context modulate the use of internal and external spatial coordinate for perception and action

2018 ◽  
Author(s):  
Virginie Crollen ◽  
Tiffany Spruyt ◽  
Pierre Mahau ◽  
Roberto Bottini ◽  
Olivier Collignon
Keyword(s):  
Coordinate System ◽  
Visual Experience ◽  
Simon Task ◽  
Frame Of Reference ◽  
The Body ◽  
Blind People ◽  
Coordinate Systems ◽  
Task Instructions ◽  
Congenitally Blind ◽  
External Frame

Recent studies proposed that the use of internal and external coordinate systems may be more flexible in congenitally blind when compared to sighted individuals. To investigate this hypothesis further, we asked congenitally blind and sighted people to perform, with the hands uncrossed and crossed over the body midline, a tactile TOJ and an auditory Simon task. Crucially, both tasks were carried out under task instructions either favoring the use of an internal (left vs. right hand) or an external (left vs. right hemispace) frame of reference. In the internal condition of the TOJ task, our results replicated previous findings (Röder et al., 2004) showing that hand crossing only impaired sighted participants’ performance, suggesting that blind people did not activate by default a (conflicting) external frame of reference. However, under external instructions, a decrease of performance was observed in both groups, suggesting that even blind people activated an external coordinate system in this condition. In the Simon task, and in contrast with a previous study (Roder et al., 2007), both groups responded more efficiently when the sound was presented from the same side of the response (‘‘Simon effect’’) independently of the hands position. This was true under the internal and external conditions, therefore suggesting that blind and sighted by default activated an external coordinate system in this task. All together, these data comprehensively demonstrate how visual experience shapes the default weight attributed to internal and external coordinate systems for action and perception depending on task demand.

Rolling Condition and Gyroscopic Moments in Curve Negotiations

2012 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Martin B. Hamper ◽  
James J. O’Shea
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
The Body ◽  
Contact Forces ◽  
Body Motion ◽  
Global Coordinate System ◽  
Gyroscopic Moment ◽  
Absolute Angular Velocity ◽  
Pure Rolling ◽  
The Stability

In vehicle system dynamics, the effect of the gyroscopic moments can be significant during curve negotiations. The absolute angular velocity of the body can be expressed as the sum of two vectors; one vector is due to the curvature of the curve, while the second vector is due to the rate of changes of the angles that define the orientation of the body with respect to a coordinate system that follows the body motion. In this paper, the configuration of the body in the global coordinate system is defined using the trajectory coordinates in order to examine the effect of the gyroscopic moments in the case of curve negotiations. These coordinates consist of arc length, two relative translations and three relative angles. The relative translations and relative angles are defined with respect to a trajectory coordinate system that follows the motion of the body on the curve. It is shown that when the yaw and roll angles relative to the trajectory coordinate system are constrained and the motion is predominantly rolling, the effect of the gyroscopic moment on the motion becomes negligible, and in the case of pure rolling and zero yaw and roll angles, the generalized gyroscopic moment associated with the system degrees of freedom becomes identically zero. The analysis presented in this investigation sheds light on the danger of using derailment criteria that are not obtained using laws of motion, and therefore, such criteria should not be used in judging the stability of railroad vehicle systems. Furthermore, The analysis presented in this paper shows that the roll moment which can have a significant effect on the wheel/rail contact forces depends on the forward velocity in the case of curve negotiations. For this reason, roller rigs that do not allow for the wheelset forward velocity cannot capture these moment components, and therefore, cannot be used in the analysis of curve negotiations. A model of a suspended railroad wheelset is used in this investigation to study the gyroscopic effect during curve negotiations.

scholarly journals Angular velocity of rotation of extended bodies in general relativity

1996 ◽  
Vol 172 ◽  
pp. 309-320
Author(s):  
S.A. Klioner
Keyword(s):  
General Relativity ◽  
Angular Velocity ◽  
Rigid Body ◽  
Rotational Motion ◽  
The Body ◽  
Astronomical Observations ◽  
Newtonian Approximation ◽  
Accurate Definition ◽  
Principal Axes ◽  
Definition Of

We consider rotational motion of an arbitrarily composed and shaped, deformable weakly self-gravitating body being a member of a system of N arbitrarily composed and shaped, deformable weakly self-gravitating bodies in the post-Newtonian approximation of general relativity. Considering importance of the notion of angular velocity of the body (Earth, pulsar) for adequate modelling of modern astronomical observations, we are aimed at introducing a post-Newtonian-accurate definition of angular velocity. Not attempting to introduce a relativistic notion of rigid body (which is well known to be ill-defined even at the first post-Newtonian approximation) we consider bodies to be deformable and introduce the post-Newtonian generalizations of the Tisserand axes and the principal axes of inertia.

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