Lecture Notes in Physics

Origins of Randomness in Mechanical Systems

By: Jaroslaw Strzalko, Juliusz Grabski, Przemyslaw Perlikowski

Write A Review

Hardcover | 16 December 2009

At a Glance

Hardcover
164 Pages

Dimensions(cm)
22.86 x 15.88 x 1.91

Hardcover

$84.99

or 4 interest-free payments of $21.25 with

or

Ships in 5 to 7 business days

Our everyday life is in?uenced by many unexpected (dif?cult to predict) events usually referred as a chance. Probably, we all are as we are due to the accumulation point of a multitude of chance events. Gambling games that have been known to human beings nearly from the beginning of our civilization are based on chance events. These chance events have created the dream that everybody can easily become rich. This pursuit made gambling so popular. This book is devoted to the dynamics of the mechanical randomizers and we try to solve the problem why mechanical device (roulette) or a rigid body (a coin or a die) operating in the way described by the laws of classical mechanics can behave in such a way and produce a pseudorandom outcome. During mathematical lessons in primary school we are taught that the outcome of the coin tossing experiment is random and that the probability that the tossed coin lands heads (tails) up is equal to 1/2. Approximately, at the same time during physics lessons we are told that the motion of the rigid body (coin is an example of suchabody)isfullydeterministic. Typically,studentsarenotgiventheanswertothe question Why this duality in the interpretation of the simple mechanical experiment is possible? Trying to answer this question we describe the dynamics of the gambling games based on the coin toss, the throw of the die, and the roulette run.

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $49.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Game Theory

The Selfish Gene

40th Anniversary edition

Paperback

RRP $32.95

$26.99

18%
OFF

The Infinite Game

From the bestselling author of Start With Why

Paperback

RRP $29.99

$24.99

17%
OFF

The Art of Strategy

A Game Theorist's Guide to Success in Business and Life

Paperback

RRP $32.95

$23.75

28%
OFF

How to Win At Chess

The Ultimate Guide for Beginners and Beyond

Hardcover

$47.75

$Math Games with Bad Drawings : 75 1/4 Simple, Challenging, Go-Anywhere Games & And Why They Matter - Ben Orlin$

Math Games with Bad Drawings

75 1/4 Simple, Challenging, Go-Anywhere Games & And Why They Matter

Hardcover

RRP $49.99

$46.99

Game Theory

2nd edition

Paperback

RRP $113.95

$96.75

15%
OFF

On the Edge

The Art of Risking Everything

Paperback

RRP $36.99

$29.75

20%
OFF

Blackjack Mathematics for Non-Mathematicians

AK Peters/CRC Recreational Mathematics Series

Hardcover

RRP $368.00

$315.99

14%
OFF

Blackjack Mathematics for Non-Mathematicians

Paperback

RRP $62.99

$60.99

Fuzzy Sets and Triangular Norms

Aggregation in Decision-Aided Intelligent Systems

Hardcover

RRP $315.00

$271.99

14%
OFF

Parabolic Problems

60 Years of Mathematical Puzzles in Parabola

Paperback

RRP $65.99

$59.75

A Course in Behavioral Economics

3rd edition

Paperback

RRP $99.99

$77.75

22%
OFF

Attack-and-Defense Games for Control Systems : Analysis and Synthesis - Huanhuan Yuan

$127.75

Introduction	p. 1
Gambling and Gaming	p. 1
A Short History	p. 2
Coin	p. 6
Dice	p. 7
Roulette	p. 11
Other Mechanical Randomizers	p. 14
Dynamics and Predictability	p. 17
Sensitive Dependence on Initial Conditions	p. 18
Fractal Basin Boundaries	p. 19
References	p. 21
General Motion of a Rigid Body	p. 23
Basic Equations of Motion of a Rigid Body	p. 23
Dynamics Equations in General Form	p. 23
Newton-Euler Equations	p. 25
Precession of a Body	p. 26
Precession of Symmetric Top	p. 27
Torque-Free Motion of Spherical Top	p. 29
Orientation of a Rigid Body	p. 30
Euler Angles and Other Conventions	p. 31
Euler's Parameters	p. 34
Air Resistance Forces and Moments	p. 35
Modeling of Bodies Impact	p. 37
References	p. 39
Equations of the Randomizer's Dynamics	p. 41
Equations of the Coin Toss	p. 41
Free Fall of a Coin	p. 41
Coin Motion in the Air	p. 46
Coin Bounces on the Floor	p. 64
Equations of the Die Throw	p. 67
Free Fall of a Die	p. 67
Die Bounces on the Table	p. 69
Equations of the Roulette Run	p. 71
Spinning Wheel Motion Analysis	p. 73
The Ball Motion on Fixed Wheel Surfaces	p. 74
Collision of the Ball with a Deflector (C_(DK))	p. 80
Free Fall of the Ball (F)	p. 83
Landing of the Ball	p. 84
Collision of the Ball with Rotating Conical Surface (C_(CC))	p. 88
Rolling of the Ball on the Spinning Wheel (R_(RC))	p. 91
The Ball Landing in the Pocket (L_(Pk))	p. 93
References	p. 95
Dynamics and Predictability	p. 97
Experimental Observations	p. 97
Simplified Models	p. 101
Keller's Model	p. 101
Precession of a Coin	p. 105
Plane Motion Model of a Cubic Die	p. 108
Nagler-Richter's Model of a Die	p. 110
Coin Tossing Simulation	p. 112
Simulations of the Die Throw	p. 117
Free Fall Probability Distribution	p. 118
Simulation of Dice Bouncing on the Table	p. 126
Simulation of the Roulette Run	p. 130
On the Predictability of Mechanical Randomizer	p. 136
References	p. 141
Nature of Randomness in Mechanical Systems	p. 143
Randomness and Determinism	p. 143
Why the Tossed Coin or Die Can Approximate the Random Process?	p. 145
Why the Impacts Induce Pseudorandomness?	p. 148
References	p. 149
Index	p. 151
Table of Contents provided by Ingram. All Rights Reserved.

Lecture Notes in Physics

Origins of Randomness in Mechanical Systems

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

More in Game Theory

The Selfish Gene

40th Anniversary edition

The Infinite Game

From the bestselling author of Start With Why

The Art of Strategy

A Game Theorist's Guide to Success in Business and Life

How to Win At Chess

The Ultimate Guide for Beginners and Beyond

Math Games with Bad Drawings

75 1/4 Simple, Challenging, Go-Anywhere Games & And Why They Matter

Game Theory

2nd edition

On the Edge

The Art of Risking Everything

Blackjack Mathematics for Non-Mathematicians

AK Peters/CRC Recreational Mathematics Series

Blackjack Mathematics for Non-Mathematicians

Fuzzy Sets and Triangular Norms

Aggregation in Decision-Aided Intelligent Systems

Parabolic Problems

60 Years of Mathematical Puzzles in Parabola

A Course in Behavioral Economics

3rd edition

Attack-and-Defense Games for Control Systems

Analysis and Synthesis

Chicago Price Theory, Second Edition

Games, Markets, and Online Learning

Game-Theoretic Models of International Crisis Bargaining

Methodological Tools in the Social Sciences

Game-Theoretic Models of International Crisis Bargaining

Methodological Tools in the Social Sciences

The "Game" for Power

Competition, Cooperation and the importance of "Networks of Power"

Combinatorial and Additive Number Theory VII

CANT, New York, USA, 2024 and 2025

On Operational Gaming, Vol. 1

A Theory with Implications for Artificial Intelligence

On Operational Gaming, Vol. 2

A Theory with Implications for Artificial Intelligence

Distributed Online Optimization and Game Theory

A History of Mathematics in Economics

From Aristotle to Artificial Intelligence

Econometrics in Theory and Practice

Analysis of Cross Section, Time Series and Panel data with STATA 18 and R

This product is categorised by