A History of Kinematics from Zeno to Einstein: on the role of motion in the development of mathematics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer
[2024]
|
| Schriftenreihe: | History of mechanism and machine science
Volume 46 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverzeichnis Seite 329-340. - Index |
| Beschreibung: | xv, 345 Seiten Illustrationen, Diagramme 24 cm |
| ISBN: | 9783031398711 |
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MARC
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| 020 | |a 9783031398711 |c hbk |9 978-3-031-39871-1 | ||
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| 100 | 1 | |a Koetsier, Teun |d 1946- |e Verfasser |0 (DE-588)139037896 |4 aut | |
| 245 | 1 | 0 | |a A History of Kinematics from Zeno to Einstein |b on the role of motion in the development of mathematics |c Teun Koetsier |
| 264 | 1 | |a Cham |b Springer |c [2024] | |
| 264 | 4 | |c ©2024 | |
| 300 | |a xv, 345 Seiten |b Illustrationen, Diagramme |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a History of mechanism and machine science |v Volume 46 | |
| 500 | |a Literaturverzeichnis Seite 329-340. - Index | ||
| 648 | 7 | |a Geschichte 490 v. Chr.-2000 |2 gnd |9 rswk-swf | |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kinematik |0 (DE-588)4030664-1 |2 gnd |9 rswk-swf |
| 653 | 0 | |a Kinematics / History | |
| 653 | 0 | |a Mathematical physics / History | |
| 653 | 0 | |a Cinématique / Histoire | |
| 653 | 0 | |a Physique mathématique / Histoire | |
| 653 | 0 | |a Kinematics | |
| 653 | 0 | |a Mathematical physics | |
| 653 | 6 | |a History | |
| 688 | 7 | |a Mathematik der Antike |0 (DE-2581)TH000007621 |2 gbd | |
| 688 | 7 | |a Bewegung |0 (DE-2581)TH000005884 |2 gbd | |
| 689 | 0 | 0 | |a Kinematik |0 (DE-588)4030664-1 |D s |
| 689 | 0 | 1 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 0 | 2 | |a Geschichte 490 v. Chr.-2000 |A z |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-031-39872-8 |
| 830 | 0 | |a History of mechanism and machine science |v Volume 46 |w (DE-604)BV022469341 |9 46 | |
| 856 | 4 | 2 | |m Digitalisierung Deutsches Museum |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034717684&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804186099271073792 |
|---|---|
| adam_text | CONTENTS
1
2
3
PHILOSOPHERS,
MATHEMATICS
AND
MOTION
.........................
1
1.1
MOTION
DOES NOT EXIST
...................................
1
1.2
MATHEMATICS
AND
THE
IDEALIST TRADITION IN GREEK
PHILOSOPHY
.............................................
5
1.3 MATHEMATICS
AND
MOTION
.................................
7
1.4
ARISTOTLE REFUTES ZENO
...................................
11
1.5
ZENO S TRICK: MOTION IS INTERPRETED
AS A
SUPER-TASK
..........
13
1.6
THE NEO-PLATONIST ONTOLOGICAL HIERARCHY
...................
15
1.7
THE POSTULATES I THROUGH 3 IN NEO-PLATONISM:
PROCLUS
SOLUTION
...............................................
17
1.8
ZEUTHEN S THESIS
........................................
19
MOTION
BEYOND THE ELEMENTS
...................................
21
2.1 THE
EUCLIDEAN CONSTRUCTION
GAME
.........................
21
2.2 THE
INCOMPLETENESS
OF THE
EUCLIDEAN CONSTRUCTION GAME
.....
24
2.3
ARCHYTAS
OF
TARENTE
......................................
26
2.4 A SOLUTION FROM PLATO S ACADEMY
.........................
28
2.5 MENAECHMUS
AND
CONIC SECTIONS
..........................
31
2.6 A REMARKABLE APPLICATION
AND
HERON S
SOLUTION
............
34
2.7
THE DOUBLING
OF
THE
CUBE: ERATOSTHENES
INSTRUMENT
.........
37
2.8 THE NEUSIS-CONSTRUCTION
AND
THE
CONCHOIDS
................
39
2.9
DIODES CISSOID
........................................
42
GENERAL
CONSIDERATIONS
AND
KINEMATICAL
ASPECTS
OF
MOTION
.......
45
3.1
PAPPUS CLASSIFICATION
...................................
45
3.2
COMPOSITION
OF
DIFFERENT UNIFORM
MOTIONS: THE
QUADRATRIX
.............................................
46
3.3
TIME-DEPENDENT KINEMATICAL ASPECTS
OF
MOTION
............
49
3.4
COMPOSITION
OF
UNIFORM MOTIONS
AND
PARADOXES
OF
MOTION IN MECHANICAL PROBLEMS
........................
51
XII CONTENTS
3.5 A REMARK
ON
METHODOLOGY
AND A
THEOREM BY ARCHIMEDES
ON
UNIFORM
MOTION
......................................
53
3.6 ARCHIMEDES: MOTION IN
GEOMETRY
.........................
57
4
KINEMATICAL MODELS IN ASTRONOMY
..............................
63
4.1 PLATO
AND
ASTRONOMY
....................................
63
4.2 THE MODEL IN PLATO S TIMAEUS
.............................
66
4.3 EUDOXUS MODELS
.......................................
69
4.4 APOLLONIUS EPICYCLE MODEL
..............................
72
4.5
HIPPARCHUS THEORY
OF
THE
MOTION
OF THE
SUN
(ABOUT 150 BCE)
.......................................
76
4.6
PTOLEMY CONTRIBUTIONS
..................................
80
4.7 PTOLEMY S
CONTRIBUTIONS CONTINUED
........................
82
4.8 ASTRONOMY IN
THE
ISLAMIC WORLD: THE TUSI-COUPLE
...........
84
5 THE BIRTH
OF
INSTANTANEOUS
VELOCITY
.............................
87
5.1 INTRODUCTION
............................................
87
5.2 VELOCITY DISTRIBUTIONS IN
SPACE
AND
TIME
...................
88
5.3 THE AVERAGE VELOCITY
OF A
ROTATING RADIUS
..................
89
5.4 THE AVERAGE VELOCITY
OF A
ROTATING DISC
....................
91
5.5 BRADWARDINE: TOWARDS
INSTANTANEOUS VELOCITY
...............
92
5.6 DUMBLETON
AND
THE
MERTON
THEOREM
.......................
94
5.7
GIOVANNI CASALI
AND
NICOLE ORESME
........................
95
5.8
ACCELERATION: EULER
AND
NEWTON S SECOND
LAW
..............
96
6 THE PARALLELOGRAM
OF
INSTANTANEOUS VELOCITIES
...................
101
6.1
INTRODUCTION
............................................
101
6.2
GILLES PERSONNE DE ROBERVAL: THE TANGENT
AS
THE
LINE
OF
INSTANTANEOUS ADVANCE
................................
102
6.3 ISAAC
NEWTON
ON
TANGENTS
................................
104
6.4 D ALEMBERT
ON
THE
PARALLELOGRAM OF INSTANTANEOUS
VELOCITIES
..............................................
108
6.5 A
PHILOSOPHICAL ASIDE
AND
KANT
ON
THE
PARALLELOGRAM
OF
VELOCITIES
............................................
109
7 NAPIER, FERMAT, DESCARTES
......................................
113
7.1 INTRODUCTION
............................................
113
7.2 JOHN NAPIER S KINEMATICAL
DEFINITION
OF
THE
LOGARITHM
AND
TORRICELLI S `LOGARITHMICA
.
............................
114
7.3 PIERRE DE FERMAT
AND
MOTION
IN HIS INTRODUCTION
TO
PLANE
AND
SOLID LOCI
..........................................
118
7.4 RENE DESCARTES
.........................................
121
7.5 DESCARTES AMBITIONS
AND
HIS NEW COMPASSES
..............
122
7.6 ALGEBRA COMES IN
.......................................
126
7.7 PAPPUS PROBLEM
........................................
127
7.8 AN EXAMPLE: THE TURNING
RULER
AND
MOVING CURVE
PROCEDURE
....................................
.......
129
CONTENTS
XIII
7.9
DESCARTES SOLUTION
OF
PAPPUS 5-LINE PROBLEM
..............
130
7.10
THE USE
OF
STRINGS
......................................
132
7.11
THE FINAL RESULTS
.......................................
133
8
DE
WITT,
VAN
SCHOOTEN, NEWTON
AND
HUYGENS
....................
135
8.1
FRANS
VAN
SCHOOTEN JUNIOR
................................
135
8.2
JAN
DE WITT
.............................................
136
8.3
FRANS
VAN
SCHOOTEN JUNIOR:
MECHANISMS
TO DRAW
A
PARABOLA
..............................................
137
8.4
FRANS
VAN
SCHOOTEN JUNIOR: MECHANISMS
TO
DRAW
AN
ELLIPSE
..............................................
139
8.5
FRANS
VAN
SCHOOTEN JUNIOR: MECHANISMS
TO
DRAW
A
HYPERBOLA
............................................
141
8.6
ISAAC NEWTON, MOTION
AND
THE
FUNDAMENTAL THEOREM
OF
THE
CALCULUS
..........................................
143
8.7
THE METHOD
OF
FLUXIONS
..................................
146
8.8
CIRCULAR
MOTION
IN
THE
WORK
OF
HUYGENS
AND
NEWTON
........
147
8.9
HUYGENS
AND
GEAR
TRAINS
.................................
151
8.9.1
LEIBNIZ
AND
TRANSCENDENTAL CURVES
..................
152
9
10
11
TOWARDS
THEORETICAL KINEMATICS
................................
155
9.1
THE INSTANTANEOUS CENTER
OF
ROTATION, DESCARTES
AND
JOHANN BERNOULLI
....................................
155
9.2
THE CYCLOID
............................................
157
9.3
THE INFLEXION CIRCLE
.....................................
159
9.4
DE LA HIRE S PROOF
......................................
160
9.5
ELLIPTIC MOTION
.........................................
162
9.6
EPICYCLOIDAL
GEARING
....................................
163
9.7
THE EULER-SAVARY FORMULA
................................
166
9.8
EULER
AND
THE
EULER-SAVARY
FORMULA
........................
169
9.9 THE
INSTANTANEOUS
AXIS
OF
ROTATION
IN
SPHERICAL
KINEMATICS
.............................................
171
9.10
GIULIO MOZZI
AND
THE
INSTANTANEOUS
SCREW AXIS
.............
173
THEORETICAL
KINEMATICS
AS A
SUBJECT
IN ITS OWN RIGHT
.............
175
10.1 INTRODUCTION
............................................
175
10.2
AUGUSTIN LOUIS CAUCHY S
1827 PAPER
......................
176
10.3
MICHEL CHARLES
.........................................
179
10.4
BOBILLIER S THEOREM
.....................................
183
10.5
JACQUES ANTOINE
CHARLES BRESSE
...........................
186
10.6
THE BALL POINTS
.........................................
189
TOWARDS
A
NEW THEORY
OF
MACHINES
............................
191
11.1
INTRODUCTION
............................................
191
11.2
LAZARE CARNOT
..........................................
193
11.3
COLLISIONS
OF
HARD
BODIES
AND
GEOMETRICAL
MOVEMENTS
.......
194
11.4
THE FIRST FUNDAMENTAL
EQUATION
...........................
195
XIV
CONTENTS
11.5 THE SECOND FUNDAMENTAL EQUATION
........................
197
11.6 GASPARD MONGE
.........................................
198
11.7 THE THEORY
OF
MACHINES IN FRANCE IN
THE
FIRST HALF
OF
THE
NINETEENTH CENTURY
................................
201
11.8 CORIOLIS VIEW
OF
MACHINES
...............................
203
11.9 AN EXAMPLE
OF A
CALCULATION
.............................
204
11.10 THE CORIOLIS FORCE
......................................
205
11.11 RICCIOLI
AND
GRIMALDI NOTICED
THE
CORIOLIS-EFFECT IN 1651
.....
209
12 THE NEW SCIENCE IS GIVEN
A
NAME: KINEMATICS
...................
211
12.1 A NEW CLASSIFICATION
OF
THE
SCIENCES
.......................
211
12.2 ROBERT WILLIS PRINCIPLES
OF
MECHANISM
....................
216
12.3 HENRI RESAL S TRAITE DE CINEMATIQUE PURE
..................
220
12.4 KINEMATICS
AS
THE
ESSENCE
OF
THEORETICAL MECHANICS
.........
223
13 DEVELOPMENTS IN KINEMATICS
OF
MECHANISMS
.....................
225
13.1 SCHEMER S PANTOGRAPH
...................................
225
13.2 THE YEAR
1784
..........................................
226
13.3 SWEET SIMPLICITY
........................................
230
13.4 EARLY THEORETICAL
INTEREST IN
WATTS
LINKAGES
................
231
13.5 PEAUCELLIER
.............................................
234
13.6 LIPMAN LIPKIN
..........................................
236
14 THE WORK
OF
ENGLISH MATHEMATICIANS
ON
LINKAGES
DURING
THE
PERIOD 1869-1878
...................................
239
14.1 CHEBYSHEV S ROLE
.......................................
239
14.2 ROBERTS WORK IN KINEMATICS BEFORE SYLVESTER S LECTURE
......
241
14.3 KEMPE S FIRST PAPER
.....................................
244
14.4 SYLVESTER S ROLE
.........................................
245
14.5 ROBERTS THEOREM
.......................................
247
14.6 SOME REMARKS ABOUT FURTHER WORK
.......................
249
14.7 CONCLUDING REMARKS
....................................
251
15 FRANZ REULEAUX, KINEMATICS
AS
THE ESSENCE
OF
MECHANICAL
ENGINEERING
..................................................
253
15.1 INTRODUCTION
............................................
253
15.2 FRANZ REULEAUX
.........................................
254
15.3 THE CENTRAL IDEA: THE KINEMATICAL
CHAIN
...................
254
15.4 INCOMPLETE PAIRS
AND
CHAINS
..............................
256
15.5
HIGHER KINEMATICAL PAIRS
.................................
257
15.6
EQUIVALENT MECHANISMS
..................................
258
15.7 EQUIVALENT ROTARY ENGINES
................................
260
15.8 ANALYSIS VERSUS SYNTHESIS
................................
260
CONTENTS
XV
16 LUDWIG BURMESTER, KINEMATICS
AS
PART
OF
GEOMETRY
..............
265
16.1 INTRODUCTION
............................................
265
16.2 BURMESTER S WORK
.......................................
266
16.3 THE LEHRBUCH DER KINEMATIK: ITS CONTENTS
..................
266
16.4 AN EXAMPLE: STEPHENSON S MOTION
........................
268
16.5 MARTIN GRUEBLER
..........................................
271
16.6 A NOTE
ON
CHEBYSHEV
....................................
273
16.7 GRUEBLER
ON
CLASSIFYING KINEMATICAL
CHAINS
.................
274
16.8 THE BURMESTER THEORY
AND
THE
BURMESTER POINTS
.............
275
16.9 ON
THE
RECEPTION
OF
BURMESTER S
WORK
.....................
279
16.10 REULEAUX CRITICISM
OF
BURMESTER
.........................
281
16.11 SOME NINETEENTH
CENTURY DEVELOPMENTS ELSEWHERE
..........
284
17 ALBERT EINSTEIN, THE
KINEMATICS
OF
SPECIAL RELATIVITY
..............
287
17.1 INTRODUCTION
............................................
287
17.2 THE PRINCIPLE
OF
RELATIVITY
................................
289
17.3 THE
PRINCIPLE
OF
THE
CONSTANCY
OF
LIGHT
AND THE
PARADOX
......
290
17.4 THE
WILLINGNESS
TO
GIVE UP
THE
AXIOM
OF
THE
ABSOLUTENESS
OF
TIME
................................................
291
17.5
CHECKING
THE
INSPIRATION
.................................
294
17.6 THE TECHNICAL DEVELOPMENT IN
THE
1905
PAPER
...............
295
17.7 DERIVATION
OF
THE
DIFFERENTIAL EQUATION
FOR
T= R(X , Y, Z,
T)
....
297
17.8 THE DETERMINATION
OF
I; (X ,
Y, Z,
T),
RL(X ,
Y, Z, T) AND
Y(X ,
Y, Z,
T)
.............................................
299
17.9 TOWARDS
THE
FORMULAE
OF
THE
LORENTZ TRANSFORMATION
.........
300
17.10 THE TWIN PARADOX
.......................................
301
18 MINKOWSKI: THE UNIVERSE
IS
A
4-DIMENSIONAL MANIFOLD
...........
303
18.1 EMPIRICISTS
AND
RATIONALISTS
..............................
303
18.2 DEVELOPMENTS
IN GEOMETRY
...............................
305
18.3 HILBERT S INFLUENCE
AND
MINKOWSKI S RATIONALISM
............
306
18.4 MINKOWSKI
AND
RELATIVITY
................................
308
18.5 A 4-DIMENSIONAL
INTERPRETATION
OF
NEWTONIAN MECHANICS
.....
309
18.6 SPECIAL RELATIVITY
DEDUCED
A
PRIORI
........................
312
18.7 THE
TWIN PARADOX
.......................................
316
19
KINEMATICS
IN
THE
20TH CENTURY
.................................
319
19.1
THE TWENTIETH CENTURY
...................................
319
19.2 INSTITUTIONALIZATION
......................................
322
19.3 TWENTIETH CENTURY MATHEMATICIANS
WORKING
IN KINEMATICS
...........................................
323
......................................................
BIBLIOGRAPHY
329
INDEX
.............................................................
341
|
| adam_txt |
CONTENTS
1
2
3
PHILOSOPHERS,
MATHEMATICS
AND
MOTION
.
1
1.1
MOTION
DOES NOT EXIST
.
1
1.2
MATHEMATICS
AND
THE
IDEALIST TRADITION IN GREEK
PHILOSOPHY
.
5
1.3 MATHEMATICS
AND
MOTION
.
7
1.4
ARISTOTLE REFUTES ZENO
.
11
1.5
ZENO'S TRICK: MOTION IS INTERPRETED
AS A
SUPER-TASK
.
13
1.6
THE NEO-PLATONIST ONTOLOGICAL HIERARCHY
.
15
1.7
THE POSTULATES I THROUGH 3 IN NEO-PLATONISM:
PROCLUS
SOLUTION
.
17
1.8
ZEUTHEN'S THESIS
.
19
MOTION
BEYOND THE ELEMENTS
.
21
2.1 THE
EUCLIDEAN CONSTRUCTION
GAME
.
21
2.2 THE
INCOMPLETENESS
OF THE
EUCLIDEAN CONSTRUCTION GAME
.
24
2.3
ARCHYTAS
OF
TARENTE
.
26
2.4 A SOLUTION FROM PLATO'S ACADEMY
.
28
2.5 MENAECHMUS
AND
CONIC SECTIONS
.
31
2.6 A REMARKABLE APPLICATION
AND
HERON'S
SOLUTION
.
34
2.7
THE DOUBLING
OF
THE
CUBE: ERATOSTHENES'
INSTRUMENT
.
37
2.8 THE NEUSIS-CONSTRUCTION
AND
THE
CONCHOIDS
.
39
2.9
DIODES' CISSOID
.
42
GENERAL
CONSIDERATIONS
AND
KINEMATICAL
ASPECTS
OF
MOTION
.
45
3.1
PAPPUS' CLASSIFICATION
.
45
3.2
COMPOSITION
OF
DIFFERENT UNIFORM
MOTIONS: THE
QUADRATRIX
.
46
3.3
TIME-DEPENDENT KINEMATICAL ASPECTS
OF
MOTION
.
49
3.4
COMPOSITION
OF
UNIFORM MOTIONS
AND
PARADOXES
OF
MOTION IN MECHANICAL PROBLEMS
.
51
XII CONTENTS
3.5 A REMARK
ON
METHODOLOGY
AND A
THEOREM BY ARCHIMEDES
ON
UNIFORM
MOTION
.
53
3.6 ARCHIMEDES: MOTION IN
GEOMETRY
.
57
4
KINEMATICAL MODELS IN ASTRONOMY
.
63
4.1 PLATO
AND
ASTRONOMY
.
63
4.2 THE MODEL IN PLATO'S TIMAEUS
.
66
4.3 EUDOXUS' MODELS
.
69
4.4 APOLLONIUS' EPICYCLE MODEL
.
72
4.5
HIPPARCHUS' THEORY
OF
THE
MOTION
OF THE
SUN
(ABOUT 150 BCE)
.
76
4.6
PTOLEMY' CONTRIBUTIONS
.
80
4.7 PTOLEMY'S
CONTRIBUTIONS CONTINUED
.
82
4.8 ASTRONOMY IN
THE
ISLAMIC WORLD: THE TUSI-COUPLE
.
84
5 THE BIRTH
OF
INSTANTANEOUS
VELOCITY
.
87
5.1 INTRODUCTION
.
87
5.2 VELOCITY DISTRIBUTIONS IN
SPACE
AND
TIME
.
88
5.3 THE AVERAGE VELOCITY
OF A
ROTATING RADIUS
.
89
5.4 THE AVERAGE VELOCITY
OF A
ROTATING DISC
.
91
5.5 BRADWARDINE: TOWARDS
INSTANTANEOUS VELOCITY
.
92
5.6 DUMBLETON
AND
THE
MERTON
THEOREM
.
94
5.7
GIOVANNI CASALI
AND
NICOLE ORESME
.
95
5.8
ACCELERATION: EULER
AND
NEWTON'S SECOND
LAW
.
96
6 THE PARALLELOGRAM
OF
INSTANTANEOUS VELOCITIES
.
101
6.1
INTRODUCTION
.
101
6.2
GILLES PERSONNE DE ROBERVAL: THE TANGENT
AS
THE
LINE
OF
INSTANTANEOUS ADVANCE
.
102
6.3 ISAAC
NEWTON
ON
TANGENTS
.
104
6.4 D'ALEMBERT
ON
THE
PARALLELOGRAM OF INSTANTANEOUS
VELOCITIES
.
108
6.5 A
PHILOSOPHICAL ASIDE
AND
KANT
ON
THE
PARALLELOGRAM
OF
VELOCITIES
.
109
7 NAPIER, FERMAT, DESCARTES
.
113
7.1 INTRODUCTION
.
113
7.2 JOHN NAPIER'S KINEMATICAL
DEFINITION
OF
THE
LOGARITHM
AND
TORRICELLI'S `LOGARITHMICA
.
.
114
7.3 PIERRE DE FERMAT
AND
MOTION
IN HIS INTRODUCTION
TO
PLANE
AND
SOLID LOCI
.
118
7.4 RENE DESCARTES
.
121
7.5 DESCARTES' AMBITIONS
AND
HIS NEW COMPASSES
.
122
7.6 ALGEBRA COMES IN
.
126
7.7 PAPPUS' PROBLEM
.
127
7.8 AN EXAMPLE: THE TURNING
RULER
AND
MOVING CURVE
PROCEDURE
.
.
129
CONTENTS
XIII
7.9
DESCARTES' SOLUTION
OF
PAPPUS' 5-LINE PROBLEM
.
130
7.10
THE USE
OF
STRINGS
.
132
7.11
THE FINAL RESULTS
.
133
8
DE
WITT,
VAN
SCHOOTEN, NEWTON
AND
HUYGENS
.
135
8.1
FRANS
VAN
SCHOOTEN JUNIOR
.
135
8.2
JAN
DE WITT
.
136
8.3
FRANS
VAN
SCHOOTEN JUNIOR:
MECHANISMS
TO DRAW
A
PARABOLA
.
137
8.4
FRANS
VAN
SCHOOTEN JUNIOR: MECHANISMS
TO
DRAW
AN
ELLIPSE
.
139
8.5
FRANS
VAN
SCHOOTEN JUNIOR: MECHANISMS
TO
DRAW
A
HYPERBOLA
.
141
8.6
ISAAC NEWTON, MOTION
AND
THE
FUNDAMENTAL THEOREM
OF
THE
CALCULUS
.
143
8.7
THE METHOD
OF
FLUXIONS
.
146
8.8
CIRCULAR
MOTION
IN
THE
WORK
OF
HUYGENS
AND
NEWTON
.
147
8.9
HUYGENS
AND
GEAR
TRAINS
.
151
8.9.1
LEIBNIZ
AND
TRANSCENDENTAL CURVES
.
152
9
10
11
TOWARDS
THEORETICAL KINEMATICS
.
155
9.1
THE INSTANTANEOUS CENTER
OF
ROTATION, DESCARTES
AND
JOHANN BERNOULLI
.
155
9.2
THE CYCLOID
.
157
9.3
THE INFLEXION CIRCLE
.
159
9.4
DE LA HIRE'S PROOF
.
160
9.5
ELLIPTIC MOTION
.
162
9.6
EPICYCLOIDAL
GEARING
.
163
9.7
THE EULER-SAVARY FORMULA
.
166
9.8
EULER
AND
THE
EULER-SAVARY
FORMULA
.
169
9.9 THE
INSTANTANEOUS
AXIS
OF
ROTATION
IN
SPHERICAL
KINEMATICS
.
171
9.10
GIULIO MOZZI
AND
THE
INSTANTANEOUS
SCREW AXIS
.
173
THEORETICAL
KINEMATICS
AS A
SUBJECT
IN ITS OWN RIGHT
.
175
10.1 INTRODUCTION
.
175
10.2
AUGUSTIN LOUIS CAUCHY'S
1827 PAPER
.
176
10.3
MICHEL CHARLES
.
179
10.4
BOBILLIER'S THEOREM
.
183
10.5
JACQUES ANTOINE
CHARLES BRESSE
.
186
10.6
THE BALL POINTS
.
189
TOWARDS
A
NEW THEORY
OF
MACHINES
.
191
11.1
INTRODUCTION
.
191
11.2
LAZARE CARNOT
.
193
11.3
COLLISIONS
OF
HARD
BODIES
AND
GEOMETRICAL
MOVEMENTS
.
194
11.4
THE FIRST FUNDAMENTAL
EQUATION
.
195
XIV
CONTENTS
11.5 THE SECOND FUNDAMENTAL EQUATION
.
197
11.6 GASPARD MONGE
.
198
11.7 THE THEORY
OF
MACHINES IN FRANCE IN
THE
FIRST HALF
OF
THE
NINETEENTH CENTURY
.
201
11.8 CORIOLIS' VIEW
OF
MACHINES
.
203
11.9 AN EXAMPLE
OF A
CALCULATION
.
204
11.10 THE CORIOLIS FORCE
.
205
11.11 RICCIOLI
AND
GRIMALDI NOTICED
THE
CORIOLIS-EFFECT IN 1651
.
209
12 THE NEW SCIENCE IS GIVEN
A
NAME: KINEMATICS
.
211
12.1 A NEW CLASSIFICATION
OF
THE
SCIENCES
.
211
12.2 ROBERT WILLIS' PRINCIPLES
OF
MECHANISM
.
216
12.3 HENRI RESAL'S TRAITE DE CINEMATIQUE PURE
.
220
12.4 KINEMATICS
AS
THE
ESSENCE
OF
THEORETICAL MECHANICS
.
223
13 DEVELOPMENTS IN KINEMATICS
OF
MECHANISMS
.
225
13.1 SCHEMER'S PANTOGRAPH
.
225
13.2 THE YEAR
1784
.
226
13.3 SWEET SIMPLICITY
.
230
13.4 EARLY THEORETICAL
INTEREST IN
WATTS
LINKAGES
.
231
13.5 PEAUCELLIER
.
234
13.6 LIPMAN LIPKIN
.
236
14 THE WORK
OF
ENGLISH MATHEMATICIANS
ON
LINKAGES
DURING
THE
PERIOD 1869-1878
.
239
14.1 CHEBYSHEV'S ROLE
.
239
14.2 ROBERTS' WORK IN KINEMATICS BEFORE SYLVESTER'S LECTURE
.
241
14.3 KEMPE'S FIRST PAPER
.
244
14.4 SYLVESTER'S ROLE
.
245
14.5 ROBERTS' THEOREM
.
247
14.6 SOME REMARKS ABOUT FURTHER WORK
.
249
14.7 CONCLUDING REMARKS
.
251
15 FRANZ REULEAUX, KINEMATICS
AS
THE ESSENCE
OF
MECHANICAL
ENGINEERING
.
253
15.1 INTRODUCTION
.
253
15.2 FRANZ REULEAUX
.
254
15.3 THE CENTRAL IDEA: THE KINEMATICAL
CHAIN
.
254
15.4 INCOMPLETE PAIRS
AND
CHAINS
.
256
15.5
HIGHER KINEMATICAL PAIRS
.
257
15.6
EQUIVALENT MECHANISMS
.
258
15.7 EQUIVALENT ROTARY ENGINES
.
260
15.8 ANALYSIS VERSUS SYNTHESIS
.
260
CONTENTS
XV
16 LUDWIG BURMESTER, KINEMATICS
AS
PART
OF
GEOMETRY
.
265
16.1 INTRODUCTION
.
265
16.2 BURMESTER'S WORK
.
266
16.3 THE LEHRBUCH DER KINEMATIK: ITS CONTENTS
.
266
16.4 AN EXAMPLE: STEPHENSON'S MOTION
.
268
16.5 MARTIN GRUEBLER
.
271
16.6 A NOTE
ON
CHEBYSHEV
.
273
16.7 GRUEBLER
ON
CLASSIFYING KINEMATICAL
CHAINS
.
274
16.8 THE BURMESTER THEORY
AND
THE
BURMESTER POINTS
.
275
16.9 ON
THE
RECEPTION
OF
BURMESTER'S
WORK
.
279
16.10 REULEAUX' CRITICISM
OF
BURMESTER
.
281
16.11 SOME NINETEENTH
CENTURY DEVELOPMENTS ELSEWHERE
.
284
17 ALBERT EINSTEIN, THE
KINEMATICS
OF
SPECIAL RELATIVITY
.
287
17.1 INTRODUCTION
.
287
17.2 THE PRINCIPLE
OF
RELATIVITY
.
289
17.3 THE
PRINCIPLE
OF
THE
CONSTANCY
OF
LIGHT
AND THE
PARADOX
.
290
17.4 THE
WILLINGNESS
TO
GIVE UP
THE
AXIOM
OF
THE
ABSOLUTENESS
OF
TIME
.
291
17.5
CHECKING
THE
INSPIRATION
.
294
17.6 THE TECHNICAL DEVELOPMENT IN
THE
1905
PAPER
.
295
17.7 DERIVATION
OF
THE
DIFFERENTIAL EQUATION
FOR
T= R(X', Y, Z,
T)
.
297
17.8 THE DETERMINATION
OF
I; (X',
Y, Z,
T),
RL(X',
Y, Z, T) AND
Y(X',
Y, Z,
T)
.
299
17.9 TOWARDS
THE
FORMULAE
OF
THE
LORENTZ TRANSFORMATION
.
300
17.10 THE TWIN PARADOX
.
301
18 MINKOWSKI: THE UNIVERSE
IS
A
4-DIMENSIONAL MANIFOLD
.
303
18.1 EMPIRICISTS
AND
RATIONALISTS
.
303
18.2 DEVELOPMENTS
IN GEOMETRY
.
305
18.3 HILBERT'S INFLUENCE
AND
MINKOWSKI'S RATIONALISM
.
306
18.4 MINKOWSKI
AND
RELATIVITY
.
308
18.5 A 4-DIMENSIONAL
INTERPRETATION
OF
NEWTONIAN MECHANICS
.
309
18.6 SPECIAL RELATIVITY
DEDUCED
A
PRIORI
.
312
18.7 THE
TWIN PARADOX
.
316
19
KINEMATICS
IN
THE
20TH CENTURY
.
319
19.1
THE TWENTIETH CENTURY
.
319
19.2 INSTITUTIONALIZATION
.
322
19.3 TWENTIETH CENTURY MATHEMATICIANS
WORKING
IN KINEMATICS
.
323
.
BIBLIOGRAPHY
329
INDEX
.
341 |
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| id | DE-604.BV049390240 |
| illustrated | Illustrated |
| index_date | 2024-07-03T23:01:07Z |
| indexdate | 2024-07-10T10:05:44Z |
| institution | BVB |
| isbn | 9783031398711 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034717684 |
| oclc_num | 1418691979 |
| open_access_boolean | |
| owner | DE-210 |
| owner_facet | DE-210 |
| physical | xv, 345 Seiten Illustrationen, Diagramme 24 cm |
| psigel | gbd_4_2402 |
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| publisher | Springer |
| record_format | marc |
| series | History of mechanism and machine science |
| series2 | History of mechanism and machine science |
| spelling | Koetsier, Teun 1946- Verfasser (DE-588)139037896 aut A History of Kinematics from Zeno to Einstein on the role of motion in the development of mathematics Teun Koetsier Cham Springer [2024] ©2024 xv, 345 Seiten Illustrationen, Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier History of mechanism and machine science Volume 46 Literaturverzeichnis Seite 329-340. - Index Geschichte 490 v. Chr.-2000 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Kinematik (DE-588)4030664-1 gnd rswk-swf Kinematics / History Mathematical physics / History Cinématique / Histoire Physique mathématique / Histoire Kinematics Mathematical physics History Mathematik der Antike (DE-2581)TH000007621 gbd Bewegung (DE-2581)TH000005884 gbd Kinematik (DE-588)4030664-1 s Mathematik (DE-588)4037944-9 s Geschichte 490 v. Chr.-2000 z DE-604 Erscheint auch als Online-Ausgabe 978-3-031-39872-8 History of mechanism and machine science Volume 46 (DE-604)BV022469341 46 Digitalisierung Deutsches Museum application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034717684&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Koetsier, Teun 1946- A History of Kinematics from Zeno to Einstein on the role of motion in the development of mathematics History of mechanism and machine science Mathematik (DE-588)4037944-9 gnd Kinematik (DE-588)4030664-1 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4030664-1 |
| title | A History of Kinematics from Zeno to Einstein on the role of motion in the development of mathematics |
| title_auth | A History of Kinematics from Zeno to Einstein on the role of motion in the development of mathematics |
| title_exact_search | A History of Kinematics from Zeno to Einstein on the role of motion in the development of mathematics |
| title_exact_search_txtP | A History of Kinematics from Zeno to Einstein on the role of motion in the development of mathematics |
| title_full | A History of Kinematics from Zeno to Einstein on the role of motion in the development of mathematics Teun Koetsier |
| title_fullStr | A History of Kinematics from Zeno to Einstein on the role of motion in the development of mathematics Teun Koetsier |
| title_full_unstemmed | A History of Kinematics from Zeno to Einstein on the role of motion in the development of mathematics Teun Koetsier |
| title_short | A History of Kinematics from Zeno to Einstein |
| title_sort | a history of kinematics from zeno to einstein on the role of motion in the development of mathematics |
| title_sub | on the role of motion in the development of mathematics |
| topic | Mathematik (DE-588)4037944-9 gnd Kinematik (DE-588)4030664-1 gnd |
| topic_facet | Mathematik Kinematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034717684&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022469341 |
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