Comparing Dynamics Initiated by an Attached Oscillating Particle for the Nonholonomic Model of a Chaplygin Sleigh and for a Model with Strong Transverse and Weak Longitudinal Viscous Friction Applied at a Fixed Point on the Body

2018 ◽  
Vol 23 (7-8) ◽  
pp. 803-820 ◽  
Author(s):  
Alexey V. Borisov ◽  
Sergey P. Kuznetsov
Keyword(s):  
Fixed Point ◽  
Viscous Friction ◽  
The Body ◽  
Chaplygin Sleigh ◽  
Strong Transverse

scholarly journals On rolling friction

2019 ◽  
Vol 485 (3) ◽  
pp. 295-299
Author(s):  
A. P. Ivanov
Keyword(s):  
Friction Coefficient ◽  
Angular Velocity ◽  
Viscous Friction ◽  
Rolling Friction ◽  
The Body ◽  
Normal Velocity ◽  
Contact Conditions ◽  
Combined Motion ◽  
Pure Rolling ◽  
Over Time

The dependence of rolling friction on velocity for various contact conditions is discussed. The principal difference between rolling and other types of relative motion (sliding and spinning) is that the points of the body in contact with the support change over time. Due to deformations, there is a small contact area and, entering into contact, the body points have a normal velocity proportional to the diameter of this area. For describing the dependence of the friction coefficient on the angular velocity in the case of “pure” rolling, a linear dependence is proposed that admits a logical explanation and experimental verification. Under the combined motion, the rolling friction retains its properties, the sliding and spinning friction acquiring the properties of viscous friction.

scholarly journals SOLUTION OF PRIVATE TASKS OF CYLINDRICAL SHEAR WAVES (in the case of the distribution of constant values γ-α + 2> 0 and α = β)

2020 ◽  
Vol 6 (334) ◽  
pp. 19-26
Author(s):  
A. Seitmuratov ◽  
◽  
M.Zh. Aitimov ◽  
A. Seitkhanova ◽  
A. Ostayeva ◽  
...  
Keyword(s):  
Fixed Point ◽  
Phase Velocity ◽  
Rheological Properties ◽  
Shear Waves ◽  
The Body ◽  
Rheological Parameters ◽  
Vibration Frequencies ◽  
Complex Phase ◽  
Wave Characteristics ◽  
Fixed Moment

Many studies usually use two methods to determine wave characteristics. First-The instantaneous state of the medium corresponding to a certain fixed moment of time is investigated. Second-The change in time of the state of the body in question at some fixed point is investigated. If studies are carried out taking into account the rheological properties of the material of the system in question or, if there is an environment surrounding the system, which also generally exhibits rheological properties, the use of these methods is significantly difficult. In such cases, the influence of rheological parameters on the components of the complex phase velocity at certain values of the vibration frequencies is studied.

scholarly journals TO THE THEORY OF n-DIMENSIONAL BRACHISTOCHRONE

2020 ◽  
pp. 53-60
Author(s):  
Gladkov S.O. ◽  
◽  
Bogdanova S.B. ◽  
Keyword(s):  
Three Dimensional ◽  
Plane Curve ◽  
Viscous Friction ◽  
Analytical Description ◽  
The Body ◽  
Viscous Drag ◽  
Friction Forces ◽  
Drag Forces ◽  
Moving Body ◽  
Plane Shape

In this paper, a solution to the problem of the motion of a brachistochrone in the ndimensional Euclidean space is firstly presented. The very first formulation of the problem in a two-dimensional case was proposed by J. Bernoulli in 1696. It represented an analytical description of the trajectory for the fastest rolling down under gravitational force only. Thereafter, a number of problems devoted to a brachistochrone were considered with account for gravitational forces, dry and viscous drag forces, and a possible variation in the mass of a moving body. Analytical solution to the formulated problem is presented in details by an example of the body moving along a brachistochrone in three-dimensional Cartesian coordinates. The obtained parametric solution is confirmed by a graphical interpretation of the calculated result. The formulated problem is solved for an ideal case when drag forces are neglected. If dry and viscous friction forces are taken into account, the plane shape of the brachistochrone remains the same,while the analysis of the solution becomes more complicated. When, for example, a side air flow is taken into account, the plane curve is replaced by a three-dimensional brachistochrone.

On the equations of rotation of a solid body about a fixed point

1864 ◽  
Vol 13 ◽  
pp. 52-64
Keyword(s):  
Fixed Point ◽  
Solid Body ◽  
The Body ◽  
Principal Axes ◽  
Usual Notation

In treating the equations of rotation of a solid body about a fixed point, it is usual to employ the principal axes of the body as the moving system of coordinates. Cases, however, occur in which it is advisable to employ other systems; and the object of the present paper is to develope the fundamental formulæ of transformation and integration for any system. Adopting the usual notation in all respects, excepting a change of sign in the quantities F, G, H, which will facilitate transformations hereafter to be made, let A = Σ m ( y 2 + z 2 ), B = Σ m ( z 2 + x 2 ), C= Σ m ( x 2 + y 2 ), -F = Σ myz , -G = Σ mzx , -H = Σ mxy ;

The Equivalence of Two Classical Problems of Free Spinning Gyrostats

1971 ◽  
Vol 38 (3) ◽  
pp. 707-708 ◽  
Author(s):  
R. E. Roberson
Keyword(s):  
Fixed Point ◽  
Constant Angular Velocity ◽  
The Body ◽  
The Other ◽  
Relative Rotation ◽  
Dynamical Equations ◽  
Interaction Torque ◽  
Axis Of Rotation ◽  
Free Body ◽  
Internal Rotor

Two problems of a torque-free body with a fixed point are considered. In both the body is rigid but for an internal rotor symmetric about its axis of rotation. In one the rotor is driven at a constant angular velocity, in the other the interaction torque between body and rotor has a zero component on the axis of relative rotation. The dynamical equations are shown to have exactly the same structure. A brief literature summary on the torque-free gyrostat is appended.

Cognitive Dance Improvisation: How Study of the Motor System Can Inspire Dance (and Vice Versa)

Leonardo ◽  
2003 ◽  
Vol 36 (3) ◽  
pp. 221-228 ◽  
Author(s):  
Ivar Hagendoorn
Keyword(s):  
Fixed Point ◽  
Cognitive Neuroscience ◽  
Motor System ◽  
Specific Capacity ◽  
Interlimb Coordination ◽  
The Body ◽  
Present Approach ◽  
Dance Improvisation ◽  
Fixed Point Technique

This paper describes several dance improvisation techniques inspired by the study of the motor system. One technique takes experiments on interlimb coordination from the laboratory to the dance studio. Another technique, termed fixed-point technique, makes use of the fact that one can change which part of the body is fixed in space. A third technique is based on the idea that one can maintain the action, as it were, by “reversing the acting limb.” All techniques target a specific capacity of the motor system and as such may inspire new psychophysical experiments. The present approach to generating movements, which merges dance improvisation with insights from cognitive neuroscience and biokinesiology, may also be fruitfully extended to robotics.

scholarly journals Is the Body Secular? Circumcision, Religious Freedom, and Bodily Integrity

2017 ◽  
Vol 18 ◽  
pp. 1
Author(s):  
Richard Amesbury
Keyword(s):  
Fixed Point ◽  
Social System ◽  
Religious Freedom ◽  
The Body ◽  
Additional Consideration ◽  
Bodily Integrity ◽  
Modern Conception ◽  
The Social ◽  
Public Debates ◽  
Free Religion

Recent legal and public debates over circumcision in Germany have tended to pit religious freedom against bodily integrity. This paper examines the background assumptions about religion and the body on which this framing depends. Insofar as the body is assumed to represent a fixed point determinable independently of ‘religion’, to frame the debate over circumcision in terms of a clash between rights pertaining respectively to religion and the body is, I argue, to circumscribe and contain religion within boundaries marked by the non-religious and non-negotiable. The secular body is thus not simply an additional consideration to be weighed against religious freedom but a condition of and limit to the modern conception of (free) religion itself. If the physical body is a synecdoche for the social system, the normative, uncircumcised body can be interpreted as standing in for the universalist order of secular law.

To the Problem of a Passive Levitation of Bodies in Physical Fields

2010 ◽  
Vol 77 (3) ◽  
Author(s):  
G. G. Denisov ◽  
V. V. Novikov ◽  
A. E. Fedorov
Keyword(s):  
Fixed Point ◽  
Point Charge ◽  
Stable Equilibrium ◽  
Domain Of Attraction ◽  
The Body ◽  
Finite Range ◽  
Asymptotic Dependence ◽  
Gyroscopic Forces ◽  
Physical Fields ◽  
The Stability

A possibility of levitation of a body carrying a point electrical charge in the field of a fixed point charge of the same sign is shown. Stabilization of an unstable equilibrium, when gravity is compensated by Coulomb’s force, is realized using gyroscopic forces generated due to the rotation of the body. A finite range of angular velocity corresponds to conservative stability of the levitating body. It is shown that dissipative and circulation forces introduced into consideration simultaneously can improve the stability of the system to asymptotic. Dependence of the domain of attraction of stable equilibrium on parameters of the system is studied numerically.

scholarly journals II. On the equations of rotation of a solid body about a fixed point

1863 ◽  
Vol 12 ◽  
pp. 523-524
Keyword(s):  
Fixed Point ◽  
Solid Body ◽  
The Body ◽  
Principal Axes

In treating the equations of rotation of a solid body about a fixed point, it is usual to employ the principal axes of the body as the moving system of coordinates. Cases, however, occur in which it is advisable to employ other systems; and the object of the present paper is to develope the fundamental formulæ of transformation and integration for any system.

THE BOUSSINESQ FORM OF SAINT VENANT'S PRINCIPLE

2000 ◽  
Vol 10 (06) ◽  
pp. 863-875
Author(s):  
EMIL O. ERNST
Keyword(s):  
Fixed Point ◽  
Elliptic System ◽  
Strain Energy ◽  
Elastic Solid ◽  
The Body ◽  
General Shape ◽  
Linear Elastic ◽  
Upper Limit ◽  
Linear Elastostatics ◽  
Fixed Part

A nonhomogeneous linear elastic solid of general shape is subjected to surface loadings vanishing outside the r-radius sphere centered in a fixed point of its border. In this paper it is proved that the upper limit of the strain energy that might be contained in a fixed part of the body goes to zero at least as rapid as a certain power of r. This result remains valid if the equations of linear elastostatics are replaced by an arbitrary second-order P.D.E. elliptic system.

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