Integrable cases of the equations of motion of a solid body situated in a potential elastic-force field

1969 ◽  
Vol 5 (4) ◽  
pp. 362-367 ◽  
Author(s):  
R. F. Ganiev
Keyword(s):  
Force Field ◽  
Solid Body ◽  
Equations Of Motion ◽  
Elastic Force

scholarly journals Force feedback delay affects perception of stiffness but not action, and the effect depends on the hand used but not on the handedness

2018 ◽  
Vol 120 (2) ◽  
pp. 781-794 ◽  
Author(s):  
Raz Leib ◽  
Inbar Rubin ◽  
Ilana Nisky
Keyword(s):  
Force Field ◽  
Grip Force ◽  
Force Feedback ◽  
Internal Representation ◽  
Elastic Force ◽  
Perceptual Bias ◽  
Load Force ◽  
Test Case ◽  
Robotic Device ◽  
Left Handed

Interaction with an object often requires the estimation of its mechanical properties. We examined whether the hand that is used to interact with the object and their handedness affected people’s estimation of these properties using stiffness estimation as a test case. We recorded participants’ responses on a stiffness discrimination of a virtual elastic force field and the grip force applied on the robotic device during the interaction. In half of the trials, the robotic device delayed the participants’ force feedback. Consistent with previous studies, delayed force feedback biased the perceived stiffness of the force field. Interestingly, in both left-handed and right-handed participants, for the delayed force field, there was even less perceived stiffness when participants used their left hand than their right hand. This result supports the idea that haptic processing is affected by laterality in the brain, not by handedness. Consistent with previous studies, participants adjusted their applied grip force according to the correct size and timing of the load force regardless of the hand that was used, the handedness, or the delay. This suggests that in all of these conditions, participants were able to form an accurate internal representation of the anticipated trajectory of the load force (size and timing) and that this representation was used for accurate control of grip force independently of the perceptual bias. Thus these results provide additional evidence for the dissociation between action and perception in the processing of delayed information. NEW & NOTEWORTHY Introducing delay to force feedback during interaction with an elastic force field biases the perceived stiffness of the force field. We show that this bias depends on the hand that was used for probing but not on handedness. At the same time, both left-handed and right-handed participants adjusted their applied grip force while using either their left or right hands in anticipation of the correct magnitude and timing despite the delay in load force.

scholarly journals Mathematical Model of Spatial Motion of the Controlled Parachute-Tether System of the Wind Kite Type

2021 ◽  
Vol 24 (4) ◽  
pp. 17-24
Author(s):  
V.M. Churkin ◽  
T.Yu. Churkina ◽  
A.M. Girin
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Solid Body ◽  
Equations Of Motion ◽  
Vertical Plane ◽  
Spatial Motion ◽  
Mathematical Task ◽  
Spatial Movement ◽  
Elastic Thread ◽  
The Mathematical Model

Mathematical modeling is created for the mathematical task of spatial motion of the controlled parachute-tether system of the “wind kite” type. The mathematical model parachute-tether system consists of a model of the main parachute and a model of the braking parachute. The parachutes are connected by the tether. The model of the main parachute is supposed to be the solid body. This solid body has two planes of symmetry. The braking parachute is the solid body with axial symmetry. The tether model is an absolutely flexible elastic thread. The tether is connected by ideal hinges with the main parachute and braking parachute. The control of the main parachute is carried out by changing the length of the control slings. Changing the length causes deformation of the dome. This is the reason for the change in its aerodynamics. Maneuvering of the main parachute occurs in the vertical plane, when the length of the control slings changes simultaneously. Maneuvering of the main parachute in space is carried out when the length of the control slings changes, when the slings are given a travel difference. The system of dynamic and kinematic equations is designed for calculating the controlled spatial movement of the main parachute, braking parachute and tether. The option exists when the mass of the tether and the forces applied to the tether cannot be neglected. The motion of the tether is represented by the equations of motion of an absolutely flexible elastic thread in projections on the axis of a natural trihedron. The mathematical model is represented by a system of ordinary differential equations and partial differential equations. The problem is solved using various numerical methods. The solution is possible with the help of an integrated numerical and analytical approach as well.

scholarly journals Analysis of the Oscillating Motion of a Solid Body on Vibrating Bearers

Machines ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 58 ◽  
Author(s):  
Bissembayev ◽  
Jomartov ◽  
Tuleshov ◽  
Dikambay
Keyword(s):  
Solid Body ◽  
Quantitative Methods ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Horizontal Displacement ◽  
Oscillatory Process ◽  
Highly Nonlinear ◽  
Cumulative Curve ◽  
The Stability ◽  
Oscillating Motion

This article considers the oscillation of a solid body on kinematic foundations, the main elements of which are rolling bearers bounded by high-order surfaces of rotation at horizontal displacement of the foundation. Equations of motion of the vibro-protected body have been obtained. It is ascertained that the obtained equations of motion are highly nonlinear differential equations. Stationary and transitional modes of the oscillatory process of the system have been investigated. It is determined that several stationary regimes of the oscillatory process exist. Equations of motion have been investigated also by quantitative methods. In this paper the cumulative curves in the phase plane are plotted, a qualitative analysis for singular points and a study of them for stability are performed. In the Hayashi plane a cumulative curve of a body protected against vibration forms a closed path which does not tend to the stability of a singular point. This means that the vibration amplitude of a body protected against vibration does not remain constant in a steady state, but changes periodically.

scholarly journals Regularization of the Equations of Motion in a Central Force-Field. Application to the Zonal Earth Satellite

1983 ◽  
Vol 74 ◽  
pp. 39-46
Author(s):  
R. Cid ◽  
S. Ferrer ◽  
A. Elipe
Keyword(s):  
Force Field ◽  
Linear Equation ◽  
Celestial Mechanics ◽  
Equations Of Motion ◽  
Hamiltonian Function ◽  
Earth Satellite ◽  
Field Application ◽  
Angular Variable ◽  
Central Force Field ◽  
Recent Method

AbstractWithin the framework of linear and regular celestial mechanics, we revise a recent method of Belen'kii (1981). We generalize some of his results, giving a new regularizing function.We make an application to the zonal earth satellite, considering the hamiltonian function through the harmonic J4. After the angular variable u has been removed, we introduce a new time and we reduce the problem to a linear equation.

scholarly journals A Novel Elastic Force-Field to Influence Mediolateral Foot Placement During Walking

2017 ◽  
Vol 25 (9) ◽  
pp. 1481-1488 ◽  
Author(s):  
Elizabeth T. Nyberg ◽  
Jordan Broadway ◽  
Christian Finetto ◽  
Jesse C. Dean
Keyword(s):  
Force Field ◽  
Elastic Force ◽  
Foot Placement

Lunar ranging experiment ephemerides and the reduction of observations (summary only)

1977 ◽  
Vol 284 (1326) ◽  
pp. 467-467
Keyword(s):  
Solid Body ◽  
Equations Of Motion ◽  
The Body ◽  
Lunar Orbit ◽  
Earth Tides ◽  
Lunar Laser Ranging ◽  
Fitting Procedure ◽  
The Earth ◽  
Starting Conditions ◽  
Tesseral Harmonics

The generation of a lunar laser ranging ephemeris uses numerical integrations of the lunar orbit and physical librations and a data fitting procedure. The relativistic equations of motion for the nine planets and the Moon are simultaneously integrated with perturbations on the lunar orbit from zonal harmonics of the Earth through degree four, lunar tesseral harmonics through degree and order three, and a tidal bulge on the Earth. The integration of the lunar rotation follows from the torques of the Earth and Sun on a solid body Moon with gravitational harmonics through degree and order three. The fitting program utilizes the integrations of the orbit and physical librations, nominal values of U.T. 1 and polar motion from the Bureau International de l’Heure, and includes corrections for atmospheric delays, nutations of the Earth’s pole taken to the body axis, solid body Earth tides, monthly and bimonthly tidal corrections in U. T. 1, and relativistic clock transformations. Not only do the fits give new starting conditions for the orbit and libration integrations but improved observatory and retroreflector coordinates, the mass ratio Sun/(Earth + Moon), and harmonics of the lunar gravity field.

Contributions of Three-body Overlap Effects to the Force Fields in CaF2-type Shell-model Lattices

1972 ◽  
Vol 27 (8-9) ◽  
pp. 1196-1210
Author(s):  
Ø. Ra
Keyword(s):  
Force Field ◽  
Shell Model ◽  
Long Range ◽  
Short Range ◽  
Equations Of Motion ◽  
Exclusion Principle ◽  
Electronic Charge ◽  
Short Range Force ◽  
Model Equations ◽  
Three Body

Abstract Due to the exclusion principle the distribution of electronic charge in an ionic crystal differs from a superposition of free-ion charge densities even in the simple Heitler-London picture. This charge density deformation engenders three-body long-range forces the influence of which on lattice vibrations is not accounted for by the usual Kellermann matrix. To obtain a better separation of long-range from short-range forces in CaF2 , SrF2, and BaF2 , i. e. to avoid absorbing long-range interactions in an adjustable short-range force field, explicit formulae are derived for three-body contributions to the shell-model equations of motion. The additional dynamical matrices pertain to arbitrary wavelengths. In adding to the force field terms which are not purely volume dependent the present descirption of three-body forces is somewhat at variance with recent work on alkali halide dynamics. The deviation from pure volume dependence originates in overlap charges residing in internuclear regions.

Sign in / Sign up

Export Citation Format

Share Document