Realistic mathematical modeling of the rattleback

Kane, T. R.; Levinson, David A.

doi:10.1016/0020-7462(82)90017-8

Cited by 31 publications

(31 citation statements)

References 3 publications

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“…Clearly equation (11) decouples from equations (12) and (13), and the solution of this first equation is given by…”

Section: Non-dimensionalisation and Solutionmentioning

confidence: 99%

“…We note that, since the horizontal velocity and spin are constant during the flight of the ball, (12) and (13) also apply in this case. Clearly there is a difference in the vertical direction and so there must be a change in equation (11).…”

Section: The Modelmentioning

confidence: 99%

“…As the oscillations start to slow down, the rattleback then starts spinning in the opposite direction. The modelling of this behaviour has been considered by a number of authors [3,8,11]. …”

Section: Introductionmentioning

confidence: 99%

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The dynamics of a bouncing superball with spin

Aston

Shail

2007

Dynamical Systems

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When a superball is thrown forwards but with backspin, it is observed to reverse both direction and spin for a few bounces before settling to bouncing motion in one direction. The bouncing ball is modelled by a two-dimensional iterated map in terms of the horizontal velocity and spin immediately after each bounce. The asymptotic motion of this system is easily determined. However, of more interest is the transient behaviour. The two-dimensional linear map is reduced to a one-dimensional nonlinear map and this map is used to determine the number of direction and spin reversals that can occur for given initial conditions. The model is then generalised to describe a ball bouncing up and down a single step or successively down a staircase.

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“…Clearly equation (11) decouples from equations (12) and (13), and the solution of this first equation is given by…”

Section: Non-dimensionalisation and Solutionmentioning

confidence: 99%

Section: The Modelmentioning

confidence: 99%

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The dynamics of a bouncing superball with spin

Aston

Shail

2007

Dynamical Systems

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“…The first scientific work on rattleback was published at the end of the 19th century [17] and it has been an object of interest till today [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], both from the point of view of dynamics and of modelling. During modelling and analysis of the Celtic stone, rolling without sliding is often assumed, leading to non-holonomic constraints [17, 21, 22, 24-26, 29, 31].…”

Section: Introductionmentioning

confidence: 99%

“…During modelling and analysis of the Celtic stone, rolling without sliding is often assumed, leading to non-holonomic constraints [17, 21, 22, 24-26, 29, 31]. Some authors assume some kind of dissipation, but far from reality [18][19][20]23]. More realistic modelling of friction is applied in the work [27].…”

Section: Introductionmentioning

confidence: 99%

Rolling resistance modelling in the Celtic stone dynamics

Awrejcewicz

Kudra

2018

Multibody Syst Dyn

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In the work there is presented a mathematical model of a rattleback lying on a horizontal plane, with special attention paid to modelling of the contact forces. Friction force modelling concerns a certain class of problems, where it is possible to assume fully developed sliding on the contact zone. The models are based on the integral expressions assuming the classical Coulomb friction law valid at each point of the contact. In order to obtain a higher simulation speed, a special class of approximations if integral functions is used, being some kind of generalization of Padé expansion. The rolling resistance is modelled as a result of special distortion of contact pressure distribution and takes into account the rolling direction and the elliptic shape of the contact. The work uses previous results of the authors, but more attention is paid to the rolling resistance model, which is extended and analysed in more detail. The models are validated experimentally and their various elements are tested.

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On the Motion of an Asymmetrical Rigid Body Rolling on a Horizontal Plane

Liu

1985

Z Angew Math Mech

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Realistic mathematical modeling of the rattleback

Cited by 31 publications

References 3 publications

The dynamics of a bouncing superball with spin

The dynamics of a bouncing superball with spin

Rolling resistance modelling in the Celtic stone dynamics

On the Motion of an Asymmetrical Rigid Body Rolling on a Horizontal Plane

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