Dynamics of Rigid Bodies with Dry Friction and Partially Elastic Collisions

1991 ◽  
pp. 57-70
Author(s):  
Michel Jean
Keyword(s):  
Dry Friction ◽  
Rigid Bodies ◽  
Elastic Collisions

scholarly journals Ternary Logic of Motion to Resolve Kinematic Frictional Paradoxes

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 620 ◽  
Author(s):  
Michael Nosonovsky ◽  
Alexander D. Breki
Keyword(s):  
Dry Friction ◽  
Sliding Friction ◽  
Rigid Bodies ◽  
Newtonian Mechanics ◽  
Stability Criteria ◽  
Ternary Logic ◽  
Elastic Bodies ◽  
Logic Approach ◽  
Frictional System ◽  
Painlevé Paradoxes

Paradoxes of dry friction were discovered by Painlevé in 1895 and caused a controversy on whether the Coulomb–Amontons laws of dry friction are compatible with the Newtonian mechanics of the rigid bodies. Various resolutions of the paradoxes have been suggested including the abandonment of the model of rigid bodies and modifications of the law of friction. For compliant (elastic) bodies, the Painlevé paradoxes may correspond to the friction-induced instabilities. Here we investigate another possibility to resolve the paradoxes: the introduction of the three-value logic. We interpret the three states of a frictional system as either rest-motion-paradox or as rest-stable motion-unstable motion depending on whether a rigid or compliant system is investigated. We further relate the ternary logic approach with the entropic stability criteria for a frictional system and with the study of ultraslow sliding friction (intermediate between the rest and motion or between stick and slip).

A system of rigid bodies with dry friction

1985 ◽  
Vol 23 (5) ◽  
pp. 497-513 ◽  
Author(s):  
M. Jean ◽  
E. Pratt
Keyword(s):  
Dry Friction ◽  
Rigid Bodies ◽  
System Of Rigid Bodies

A theorem on elastic collisions between ideal rigid bodies

1989 ◽  
Vol 57 (2) ◽  
pp. 121-125 ◽  
Author(s):  
Frank S. Crawford
Keyword(s):  
Rigid Bodies ◽  
Elastic Collisions

scholarly journals Spinning rigid bodies driven by orbital forcing: the role of dry friction

2022 ◽  
Author(s):  
Pablo de Castro ◽  
Tiago Araújo Lima ◽  
Fernando Parisio
Keyword(s):  
Dry Friction ◽  
Rigid Bodies ◽  
Orbital Forcing

scholarly journals Impedance of rigid bodies in one-dimensional elastic collisions

2012 ◽  
Vol 34 (1) ◽  
Author(s):  
Janilo Santos ◽  
Bruna P.W. de Oliveira ◽  
Osman Rosso Nelson
Keyword(s):  
Energy Transfer ◽  
Impedance Matching ◽  
Maximum Energy ◽  
Rigid Bodies ◽  
Energy Transmission ◽  
Elastic Collisions ◽  
One Dimensional ◽  
Oscillatory Systems ◽  
System Of Rigid Bodies

In this work we study the problem of one-dimensional elastic collisions of billiard balls, considered as rigid bodies, in a framework very different from the classical one presented in text books. Implementing the notion of impedance matching as a way to understand efficiency of energy transmission in elastic collisions, we find a solution which frames the problem in terms of this conception. We show that the mass of the ball can be seen as a measure of its impedance and verify that the problem of maximum energy transfer in elastic collisions can be thought of as a problem of impedance matching between different media. This approach extends the concept of impedance, usually associated with oscillatory systems, to system of rigid bodies.

scholarly journals A Two-Dimensional Discrete Model for Dynamic Analysis of Belt Transmission with Dry Friction

2014 ◽  
Vol 61 (4) ◽  
pp. 571-593
Author(s):  
Krzysztof Kubas
Keyword(s):  
Dynamic Analysis ◽  
Dry Friction ◽  
Discrete Model ◽  
Equations Of Motion ◽  
Friction Model ◽  
Rigid Bodies ◽  
Friction Forces ◽  
Calculation Results ◽  
Model Of Friction ◽  
Belt Transmission

Abstract The paper presents a model for dynamic analysis of belt transmission. A twodimensional discrete model was assumed of a belt consisting of rigid bodies joined by translational and torsion spring-damping elements. In the model, both a contact model and a dry friction model including creep were taken into consideration for belt-pulley interaction. A model with stiffness and damping between the contacting surfaces was used to describe the contact phenomenon, whereas a simplified model of friction was assumed. Motion of the transmission is triggered under the influence of torque loads applied on the pulleys. Equations of motion of separate elements of the belt and pulleys were solved numerically by using adaptive stepsize integration methods. Calculation results are presented of the reaction forces acting on the belt as well as contact and friction forces between the belt body and pulley in the sample of the belt transmission. These were obtained under the influence of the assumed drive and resistance torques.

scholarly journals Spinning Rigid Bodies Driven by Orbital Forcing: The Role of Dry Friction

2021 ◽  
Author(s):  
Pablo de Castro ◽  
Tiago Araújo Lima ◽  
Fernando Parisio
Keyword(s):  
Rigid Body ◽  
Dry Friction ◽  
Initial Conditions ◽  
Rigid Bodies ◽  
The Body ◽  
Driving Frequency ◽  
Orbital Forcing ◽  
Highly Nonlinear ◽  
Dynamical Regimes ◽  
Body Shapes

Abstract A ``circular orbital forcing'' makes a chosen point on a rigid body follow a circular motion while the body spins freely around that point. We investigate this problem for the planar motion of a body subject to dry friction. We focus on the effect called \emph{reverse rotation} (RR), where spinning and orbital rotations are antiparallel. Similar reverse dynamics include the rotations of Venus and Uranus, journal machinery bearings, tissue production reactors, and chiral active particles. Due to dissipation, RRs are possible only as a transient. Here the transient or \emph{flip} time $t_\textrm{f}$ depends on the circular driving frequency $\omega$, unlike the viscous case previously studied. We find $t_\textrm{f}\sim\omega^{\gamma-1}\mu^{-\gamma/2}$, where $\mu$ is the friction coefficient and $\gamma=0$ ($\gamma=2$) for low (high) $\omega$. Whether RRs really occur depends on the initial conditions as well as on $\mu$ and $H$, a geometrical parameter. The critical $H_\textrm{c}(\mu)$ where RRs become possible follows a $q$-exponential with $q\simeq1.9$, a more restrictive RR scenario than in the wet case. We use animations to visualize the different dynamical regimes that emerge from the highly nonlinear dissipation mechanism of dry friction. Our results are valid across multiple investigated rigid body shapes.

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