Different Models of Rolling for a Robot Ball on a Plane as a Generalization of the Chaplygin Ball Problem

2019 ◽  
Vol 24 (5) ◽  
pp. 560-582 ◽  
Author(s):  
Ivan A. Bizyaev ◽  
Alexey V. Borisov ◽  
Ivan S. Mamaev
Keyword(s):  
Chaplygin Ball ◽  
Ball Problem

Motion periodicity and bifurcation of a wave excited hopping ball

2019 ◽  
Vol 475 (2228) ◽  
pp. 20190137
Author(s):  
Gaurang Ruhela ◽  
Anirvan DasGupta
Keyword(s):  
Wave Amplitude ◽  
Harmonic Wave ◽  
Inelastic Collisions ◽  
Loss Of Stability ◽  
Elastic Surface ◽  
Minimum Frequency ◽  
Surface Motion ◽  
Return Map ◽  
Ball Problem ◽  
Subsequent Loss

We consider the problem of a hopping ball excited by a travelling harmonic wave on an elastic surface. The ball, considered as a particle, is assumed to interact with the surface through inelastic collisions. The surface motion due to the wave induces a horizontal drift in the ball. The problem is treated analytically under certain approximations. The phase space of the hopping motion is captured by constructing a phase-velocity return map. The fixed points of the return map and its compositions represent periodic hopping solutions. The linear stability of the obtained periodic solution is studied in detail. The minimum frequency for the onset of periodic hops, and the subsequent loss of stability at the bifurcation frequency, have been determined analytically. Interestingly, for small values of wave amplitude, the analytical solutions reveal striking similarities with the results of the classical bouncing ball problem.

scholarly journals Chaplygin ball over a fixed sphere: an explicit integration

2008 ◽  
Vol 13 (6) ◽  
pp. 557-571 ◽  
Author(s):  
A. V. Borisov ◽  
Yu. N. Fedorov ◽  
I. S. Mamaev
Keyword(s):  
Explicit Integration ◽  
Chaplygin Ball

EXPRESS: Fooling System 1 in the field of perception: Failure to Intuitively Detect Attribute Substitution in the Flushtration Count Illusion

2021 ◽  
pp. 174702182110693
Author(s):  
Cyril Thomas ◽  
Marion Botella ◽  
André Didierjean
Keyword(s):  
Human Brain ◽  
Cognitive Style ◽  
Cognitive Reflection Test ◽  
Substitution Error ◽  
Perceptual Illusion ◽  
Cognitive Reflection ◽  
Ball Problem ◽  
Perceptual Attribute ◽  
System 1 ◽  
The Relationship

To facilitate our interactions with the surroundings, the human brain sometimes reshapes the situations that it faces in order to simplify them. This phenomenon has been widely studied in the context of reasoning, especially through the attribute substitution error. It has however been given much less attention in the field of perception. Recent research on the bat-and-ball problem suggests that reasoners are able to intuitively detect attribute substitution errors. Using a perceptual illusion drawn from the field of magic, we investigate the extent to which a perceptual form of attribute substitution depends on executive resources and can be detected. We also investigate the relationship between susceptibility to attribute substitution error in the flushtration count illusion and in a French adaptation of the bat-and ball problem. Finally, we investigate the link between the intuitive cognitive style (assessed by the Cognitive Reflection Test) and the susceptibility to the flushtration count illusion. Our results suggest that participants do not detect perceptual attribute substitution error, that this phenomenon could be independent of the executive resources allocated to the task, and could rest on mechanisms distinct from those that produce errors in reasoning. We discuss differences between these two phenomena, and factors that may explain them.

Stick-Slip, Imposition-Removal of Constraints and the Spinning Ball Problem

2000 ◽  
Vol 67 (4) ◽  
pp. 720-726
Author(s):  
S. Djerassi
Keyword(s):  
Computer Program ◽  
Experimental Results ◽  
Stick Slip ◽  
Elastic Bodies ◽  
Cyclic Motion ◽  
Ball Problem

It has been observed that balls pressed between elastic bodies spin when subjected to linear, cyclic motion. This paper proposes an explanation to this phenomenon, based upon the stick-slip theory. To this end, a modified, vectorial formulation of the stick-slip theory is presented. The formulation is applied to a model comprising a ball pressed between pairs of springs and dampers. A computer program based on this formulation is used to predict the resulting motion. Predictions are shown to agree with experimental results. [S0021-8936(01)00701-2]

scholarly journals Second-guess: Testing the specificity of error detection in the bat-and-ball problem

2019 ◽  
Vol 193 ◽  
pp. 214-228 ◽  
Author(s):  
Bence Bago ◽  
Matthieu Raoelison ◽  
Wim De Neys
Keyword(s):  
Error Detection ◽  
Ball Problem
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