A History of Kinematics from Zeno to Einstein : On the Role of Motion in the Development of Mathematics / by Teun Koetsier.

Format:

Book

Author/Creator:

Koetsier, T.

Series:

History of Mechanism and Machine Science, 1875-3426 ; 46

Language:

English

Subjects (All):

Mathematics.

History.

Science--History.

Science.

Mechanical engineering.

History of Mathematical Sciences.

History of Science.

Mechanical Engineering.

Local Subjects:

History of Mathematical Sciences.

History of Science.

Mechanical Engineering.

Physical Description:

1 online resource (354 pages)

Edition:

1st ed. 2024.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2024.

Summary:

This book covers the history of kinematics from the Greeks to the 20th century. It shows that the subject has its roots in geometry, mechanics and mechanical engineering and how it became in the 19th century a coherent field of research, for which Ampère coined the name kinematics. The story starts with the important Greek tradition of solving construction problems by means of kinematically defined curves and the use of kinematical models in Greek astronomy. As a result in 17th century mathematics motion played a crucial role as well, and the book pays ample attention to it. It is also discussed how the concept of instantaneous velocity, unknown to the Greeks, etc was introduced in the late Middle Ages and how in the 18th century, when classical mechanics was formed, kinematical theorems concerning the distribution of velocity in a solid body moving in space were proved. The book shows that in the 19th century, against the background of the industrial revolution, the theory of machines and thus the kinematics of mechanisms received a great deal of attention. In the final analysis, this led to the birth of the discipline.

Contents:

Intro

Preface

Contents

1 Philosophers, Mathematics and Motion

1.1 Motion Does Not Exist

1.2 Mathematics and the Idealist Tradition in Greek Philosophy

1.3 Mathematics and Motion

1.4 Aristotle Refutes Zeno

1.5 Zeno's Trick: Motion Is Interpreted as a Super-Task

1.6 The Neo-platonist Ontological Hierarchy

1.7 The Postulates 1 Through 3 in Neo-platonism: Proclus Solution

1.8 Zeuthen's Thesis

2 Motion Beyond the Elements

2.1 The Euclidean Construction Game

2.2 The Incompleteness of the Euclidean Construction Game

2.3 Archytas of Tarente

2.4 A Solution from Plato's Academy

2.5 Menaechmus and Conic Sections

2.6 A Remarkable Application and Heron's Solution

2.7 The Doubling of the Cube: Eratosthenes' Instrument

2.8 The Neusis-Construction and the Conchoids

2.9 Diocles' Cissoid

3 General Considerations and Kinematical Aspects of Motion

3.1 Pappus' Classification

3.2 Composition of Different Uniform Motions: The Quadratrix

3.3 Time-Dependent Kinematical Aspects of Motion

3.4 Composition of Uniform Motions and Paradoxes of Motion in Mechanical Problems

3.5 A Remark on Methodology and a Theorem by Archimedes on Uniform Motion

3.6 Archimedes: Motion in Geometry

4 Kinematical Models in Astronomy

4.1 Plato and Astronomy

4.2 The Model in Plato's Timaeus

4.3 Eudoxus' Models

4.4 Apollonius' Epicycle Model

4.5 Hipparchus' Theory of the Motion of the Sun (About 150 BCE)

4.6 Ptolemy' Contributions

4.7 Ptolemy's Contributions Continued

4.8 Astronomy in the Islamic World: The Tusi-Couple

5 The Birth of Instantaneous Velocity

5.1 Introduction

5.2 Velocity Distributions in Space and Time

5.3 The Average Velocity of a Rotating Radius

5.4 The Average Velocity of a Rotating Disc

5.5 Bradwardine: Towards Instantaneous Velocity.

5.6 Dumbleton and the Merton Theorem

5.7 Giovanni Casali and Nicole Oresme

5.8 Acceleration: Euler and Newton's Second Law

6 The Parallelogram of Instantaneous Velocities

6.1 Introduction

6.2 Gilles Personne de Roberval: The Tangent as the Line of Instantaneous Advance

6.3 Isaac Newton on Tangents

6.4 D'Alembert on the Parallelogram of Instantaneous Velocities

6.5 A Philosophical Aside and Kant on the Parallelogram of Velocities

7 Napier, Fermat, Descartes

7.1 Introduction

7.2 John Napier's Kinematical Definition of the Logarithm and Torricelli's 'Logarithmica'

7.3 Pierre de Fermat and Motion in His Introduction to Plane and Solid Loci

7.4 René Descartes

7.5 Descartes' Ambitions and His New Compasses

7.6 Algebra Comes In

7.7 Pappus' Problem

7.8 An Example: The Turning Ruler and Moving Curve Procedure

7.9 Descartes' Solution of Pappus' 5-Line Problem

7.10 The Use of Strings

7.11 The Final Results

8 De Witt, van Schooten, Newton and Huygens

8.1 Frans van Schooten Junior

8.2 Jan de Witt

8.3 Frans van Schooten Junior: Mechanisms to Draw a Parabola

8.4 Frans van Schooten Junior: Mechanisms to Draw an Ellipse

8.5 Frans van Schooten Junior: Mechanisms to Draw a Hyperbola

8.6 Isaac Newton, Motion and the Fundamental Theorem of the Calculus

8.7 The Method of Fluxions

8.8 Circular Motion in the Work of Huygens and Newton

8.9 Huygens and Gear Trains

8.9.1 Leibniz and Transcendental Curves

9 Towards Theoretical Kinematics

9.1 The Instantaneous Center of Rotation, Descartes and Johann Bernoulli

9.2 The Cycloid

9.3 The Inflexion Circle

9.4 De La Hire's Proof

9.5 Elliptic Motion

9.6 Epicycloidal Gearing

9.7 The Euler-Savary Formula

9.8 Euler and the Euler-Savary Formula

9.9 The Instantaneous Axis of Rotation in Spherical Kinematics.

9.10 Giulio Mozzi and the Instantaneous Screw Axis

10 Theoretical Kinematics as a Subject in Its Own Right

10.1 Introduction

10.2 Augustin Louis Cauchy's 1827 Paper

10.3 Michel Chasles

10.4 Bobillier's Theorem

10.5 Jacques Antoine Charles Bresse

10.6 The Ball Points

11 Towards a New Theory of Machines

11.1 Introduction

11.2 Lazare Carnot

11.3 Collisions of Hard Bodies and Geometrical Movements

11.4 The First Fundamental Equation

11.5 The Second Fundamental Equation

11.6 Gaspard Monge

11.7 The Theory of Machines in France in the First Half of the Nineteenth Century

11.8 Coriolis' View of Machines

11.9 An Example of a Calculation

11.10 The Coriolis Force

11.11 Riccioli and Grimaldi Noticed the Coriolis-Effect in 1651

12 The New Science Is Given a Name: Kinematics

12.1 A New Classification of the Sciences

12.2 Robert Willis' Principles of Mechanism

12.3 Henri Résal's Traité de Cinématique Pure

12.4 Kinematics as the Essence of Theoretical Mechanics

13 Developments in Kinematics of Mechanisms

13.1 Scheiner's Pantograph

13.2 The Year 1784

13.3 Sweet Simplicity

13.4 Early Theoretical Interest in Watts Linkages

13.5 Peaucellier

13.6 Lipman Lipkin

14 The Work of English Mathematicians on Linkages during the Period 1869-1878

14.1 Chebyshev's Role

14.2 Roberts' Work in Kinematics Before Sylvester's Lecture

14.3 Kempe's First Paper

14.4 Sylvester's Role

14.5 Roberts' Theorem

14.6 Some Remarks About Further Work

14.7 Concluding Remarks

15 Franz Reuleaux, Kinematics as the Essence of Mechanical Engineering

15.1 Introduction

15.2 Franz Reuleaux

15.3 The Central Idea: The Kinematical Chain

15.4 Incomplete Pairs and Chains

15.5 Higher Kinematical Pairs

15.6 Equivalent Mechanisms

15.7 Equivalent Rotary Engines.

15.8 Analysis Versus Synthesis

16 Ludwig Burmester, Kinematics as Part of Geometry

16.1 Introduction

16.2 Burmester's Work

16.3 The Lehrbuch der Kinematik: Its Contents

16.4 An Example: Stephenson's Motion

16.5 Martin Grübler

16.6 A Note on Chebyshev

16.7 Grübler on Classifying Kinematical Chains

16.8 The Burmester Theory and the Burmester Points

16.9 On the Reception of Burmester's Work

16.10 Reuleaux' Criticism of Burmester

16.11 Some Nineteenth Century Developments Elsewhere

17 Albert Einstein, the Kinematics of Special Relativity

17.1 Introduction

17.2 The Principle of Relativity

17.3 The Principle of the Constancy of Light and the Paradox

17.4 The Willingness to Give Up the Axiom of the Absoluteness of Time

17.5 Checking the Inspiration

17.6 The Technical Development in the 1905 Paper

17.7 Derivation of the Differential Equation for τ = τ(xʹ, y, z, t)

17.8 The Determination of ξ(xʹ, y, z, t), η(xʹ, y, z, t) and ζ(xʹ, y, z, t)

17.9 Towards the Formulae of the Lorentz Transformation

17.10 The Twin Paradox

18 Minkowski: The Universe Is a 4-Dimensional Manifold

18.1 Empiricists and Rationalists

18.2 Developments in Geometry

18.3 Hilbert's Influence and Minkowski's Rationalism

18.4 Minkowski and Relativity

18.5 A 4-Dimensional Interpretation of Newtonian Mechanics

18.6 Special Relativity Deduced a Priori

18.7 The Twin Paradox

19 Kinematics in the 20th Century

19.1 The Twentieth Century

19.2 Institutionalization

19.3 Twentieth Century Mathematicians Working in Kinematics

Bibliography

Index.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-031-39872-6

OCLC:

1402032875