History of virtual work laws: a history of mechanics prospective
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Milan [u.a.]
Birkhäuser
2012
|
| Schriftenreihe: | Science networks, historical studies
42 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024811390&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XII, 492 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9788847020559 9788847020016 |
Internformat
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| 020 | |a 9788847020559 |9 978-88-470-2055-9 | ||
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| 100 | 1 | |a Capecchi, Danilo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a History of virtual work laws |b a history of mechanics prospective |c Danilo Capecchi |
| 264 | 1 | |a Milan [u.a.] |b Birkhäuser |c 2012 | |
| 300 | |a XII, 492 S. |b Ill., graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Science networks, historical studies |v 42 | |
| 648 | 7 | |a Geschichte 350 v. Chr.-1910 |2 gnd |9 rswk-swf | |
| 648 | 7 | |a Geschichte 350 v. Chr.-2010 |2 gnd |9 rswk-swf | |
| 650 | 0 | 7 | |a Mechanik |0 (DE-588)4038168-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Mechanik |0 (DE-588)4038168-7 |D s |
| 689 | 0 | 1 | |a Geschichte 350 v. Chr.-1910 |A z |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Mechanik |0 (DE-588)4038168-7 |D s |
| 689 | 1 | 1 | |a Geschichte 350 v. Chr.-2010 |A z |
| 689 | 1 | |8 1\p |5 DE-604 | |
| 830 | 0 | |a Science networks, historical studies |v 42 |w (DE-604)BV002495563 |9 42 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024811390&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-024811390 | |
Datensatz im Suchindex
| _version_ | 1819314179960471552 |
|---|---|
| adam_text | Contents
1
Introduction
................................................. 1
1.1 Virtual
velocity laws
..................................... 2
1 .2
Virtual displacement laws
................................. 4
1.3
Virtual work laws as principles of mechanics
................. 5
1.4
Virtual work laws as theorems of mechanics
................. 9
1.5
Contemporary tendencies
................................. 10
1.6
Final remarks. The rational justification of virtual work laws
.... 12
2
Logic status of virtual work laws
............................... 15
2.1
The theorem of virtual work
............................... 17
2.1.1
Proofs of the virtual work theorems in the literature
___ 23
2.1
Л
. 1
Physics and rational mechanics treatises
...... 23
2.1.
1.2
Statics handbooks
........................ 24
2.1.1.3
Poinsot s proof
........................... 26
2.2
The principle of virtual work
.............................. 27
2.2.1
Force as a primitive concept
........................ 28
2.2.1.
1 Equilibrium ease
......................... 28
2.2.1.2
Motion case
............................. 29
2.2.2
Work as a primitive concept
........................ 31
2.2.2.
1 Equilibrium case
......................... 31
2.2.2.2
Motion case
............................. 32
3
Greek origins
................................................ 33
3.1
Different approaches to the law of the lever
.................. 34
3.1.1
Aristotelian mechanics
............................ 34
3.1.1.1
Physica and
De cáelo
..................... 35
3.1.1.2
Mechanica
problematu
.................... 38
3.1.1.3
A law of virtual work
..................... 43
3.1.2
Archimedean mechanics
-----....................... 45
3.1.2.1
Proof of the law of the lever
................ 48
3.2
The mechanics of Hero of Alexandria
....................... 51
viii Contents
3.2.1
The principles of Hero
s
mechanics
................. 53
3.2.1.1
A law of virtual work
..................... 55
3.2.1.2
Hero s inclined plane law
.................. 58
3.3
The mechanics of Pappus of Alexandria
..................... 59
3.3.1
Pappus inclined plane law
......................... 60
4
Arabic and Latin science of weights
............................ 63
4.1
Arabic mechanics
........................................ 66
4.1.1
Weight as an active factor in Arabic mechanics
....... 68
4.1.1.1
Liber karastonis
.......................... 69
4.1.1.2
Kitab al-Qarastun
........................ 73
4.1.2
Comments on the Arabic virtual work law
............ 74
4.2
Latin mechanics
......................................... 75
4.2.1
Weight as a passive factor in the Latin mechanics
...... 80
4.2.2
Propositions
..................................... 80
4.2.2.1
Proposition 1
............................. 81
4.2.2.2
Proposition II
............................ 84
4.2.2.3
Proposition VI. The law of the Lever
........ 86
4.2.2.4
Proposition
VIII.......................... 86
4.2.2.5
Proposition X. The law of the inclined plane
.. 88
4.2.3
Comments on the Latin virtual work law
............. 89
5
Italian Renaissance statics
..................................... 91
5.1
Renaissance engineering
.................................. 95
5.1.1 Daniele
Barbaro
and Buonaiuto Lorini
............... 96
5.2
Nicolo Tartaglia.........................................
97
5.2.1
Definitions and petitions
........................... 98
5.2.2
Propositions
..................................... 98
5.2.2.1
Proof of propositions I-IV
................. 100
5.2.2.2
The law of the lever
....................... 101
5.2.2.3
The law of the inclined plane
............... 103
5.3
Girolamo
Cardano
....................................... 104
5.3.1
De subtitilate
.................................... 105
5.3.2
De opus
novum .................................. 107
5.4
Guidobaldo
dal Monte
.................................... 108
5.4.1
The centre
of gravity..............................
109
5.4.2
The balance
..................................... 109
5.4.3
The virtual work law
.............................. 115
5.5
Giovanni
Battista Benedetti ...............................
116
5.5.1
Effect of the position of a weight on its heaviness
...... 116
5.5.2
Errors of
Tartaglia
and Jordanus
.................... 118
5.6
Galileo Galilei
.......................................... 120
5.6.
1 The concept of moment. A law of virtual velocities
.... 121
5.6.2
A law of virtual displacements
...................... 127
5.6.3
Proof of the law of the inclined plane
................ 131
Contents ix
Torricelli s principle..........................................
135
6.1
The centrobaric
.......................................... 135
6.2
Galileo s
centrobaric..................................... 138
6.3 Torricelli s
joined heavy bodies
............................ 140
6.3.1
Torricelli s fundamental concepts on the centre of gravity
141
6.4
Torricelli s principle
..................................... 144
6.4.1
Analysis of the aggregate of two bodies
.............. 146
6.4.2
Torricelli s principle as a criterion of equilibrium
...... 148
6.5
Evolution of Torricelli s principle. Its role in virtual work laws
.. 153
6.5.1
A restricted form of Torricelli s principle
............. 154
European statics during the
XVI
and
XVII
centuries
............. 157
7.1
French statics
........................................... 157
7.1.1
Gille
Personne de Roberval
........................ 160
7.1.1.1
The inclined plane law
.................... 160
7.
1.
1.2
The rule of the parallelogram
............... 161
7.1.2 René
Descartes
................................... 164
7.1.2.1
The concept of force
...................... 164
7.1.2.2
The application to simple machines
.......... 167
7.1.2.3
The refusal of virtual velocities
.............
1
70
7.1.2.4
Displacements at the very beginning of motion
171
7.1.2.5
A possible precursor
...................... 173
7.1.3
Blaise Pascal
.................................... 175
7.1.4
Post Cartesians
................................... 176
7.2
Nederland
statics
........................................ 177
7.2.1
Simon Stevin
.................................... 178
7.2.
1
.1
The rule of the parallelogram of forces
.......
1
80
7.2.1.2
The law of virtual work
.................... 184
7.2.2
Christiaan Huygens
...............................
1
87
7.3
British statics
........................................... 189
7.3.1
John
Wallis
...................................... 190
7.3.2
Isaac Nevton
..................................... 193
The principle of virtual velocities
.............................. 195
8.
1 The concept of force in the X
VIH
century
.................... 195
8.1.1
Newtonian concept of force
........................ 195
8.1.2
Leibnizian concept of force
........................ 197
8.2
Johann
Bernoulli mechanics
............................... 199
8.2.1
Dead and living forces according to Bernoulli
......... 199
8.2.2
The rule of energies
............................... 201
8.3
Varignon: the rule of energies and the law of composition
offerees
.........................................-...... 210
8.3.1
Elements of Varignon
s
mechanics
.................. 210
8.3.2
The rule of the parallelogram versus the rule of energies
213
χ
Contents
9
The Jesuit school of the
XVIII
century
.......................... 217
9.1
Vincenzo AngiulH
and
Vincenzo
Riccati
..................... 218
9.1.1
The principle of actions of
Vincenzo Angiulli
......... 218
9.1.1.1
The action of a force
...................... 219
9.1.1.2
The principle of actions
................... 221
9.1.1.3
The measure of actions
................... 223
9.1
Л
.4
The principle of action and the principles of
statics
.................................. 225
9.1
Л
.5
The applications to simple machines
......... 228
9
Л
.2
The principle of actions of
Vincenzo
Riccati
.......... 230
9.2
Ruggiero Giuseppe Boscovich
............................. 233
9.2.1
A virtual work law for Saint Peter s dome
............ 234
9.2.1.1
The mechanism of failure and the forces
..... 235
10
Lagrange s contribution
...................................... 237
10.1
First introduction of the virtual velocity principle
............. 240
10.1.1
The first ideas about a new principle of mechanics
..... 240
10.1.2
Recherches sur la Vibration de la Lune
............... 242
10.1.2.1
Setting of the astronomical problem
......... 245
10.1.2.2
The symbolic equation of dynamics
......... 247
10.1.2.3
The virtual velocity principle
............... 250
10.1.3
The
Théorie de la lïhration de la Lune
............... 251
10.2
Méchanique analitique and Mécanique analytique
............ 252
Í0.2.1
Méchanique
analitique
............................ 253
10.2.1.1
Constraint reactions
....................... 258
10.2.2
Mécanique analytique
............................. 259
10.2.2.1
Criticisms of
Lagrange s
proof.............
263
10.3
The Théorie des fonctions analytiques
....................... 264
10.4
Generalizations of the virtual velocity principle to dynamics
.... 268
10.4.1
The calculus of variations
.......................... 273
10.4.2
Elements of D Alembert s mechanics
................ 274
10.4.2.1
D Alembert principle
..................... 277
11
Lazare
Carnot s mechanics of collision
......................... 281
11.1
Carnot s laws of mechanics
................................ 285
11.1.1
The first fundamental equation of mechanics
.......... 287
11
.1.2
Geometric motions
............................... 289
11.1.3
The second fundamental equation of mechanics
....... 291
1
1.2
Gradual changing of motion. A law of virtual work
............ 293
11.3
The moment of activity
................................... 295
12
The debate in Italy
....................................■...... 299
12
Л
The criticisms on the evidence of the principle
................ 300
12.1.1
Vittorio
Fossombroni
............................. 300
12.1.1.1
Invariable distance systems
................ 301
Contents
xi
12.1.1.2
The equation of forces
..................... 302
12.1.1.3
The equation of moments
.................. 304
12.1.2
Girolamo
Saladini
................................ 306
12.1.3
François
Joseph Servois
........................... 308
12.2
The criticisms on the use of infinitesimals
.................... 311
12.2.1
Gabrio
Piola
..................................... 312
12.2.1.1
Piola s principles of material point mechanics
. 312
12.2.1.2
System of free material points
.............. 314
12.2.1.3
System of constrained material points
........ 315
13
The debate at the
École polytechnique..........................
317
13.1
One of the first professor of mechanics.
Gaspard de Prony
...... 319
13.1.1
Proof from the composition of forces rule
............ 320
13.2
Joseph Fourier
.......................................... 321
13.2.
1 First proof
....................................... 323
13.2.2
Second proof
.................................... 325
13.2.3
Third proof
...................................... 326
13.3
André
Marie Ampere
..................................... 328
13.4
Pierre Simon Laplace
..................................... 332
14
Poinsot s
criticism
............................................ 335
14.1
Considerations
sur le principe des vitesses virtuelles
.......... 336
14.2
Théorie générale de l éifuilibre et du mouvement des systèmes
.,
33e)
14.2.1
Poinsoťs
principles of mechanics
................... 342
14.2.
1
.1
System of material points constrained by a
unique equation
.......................... 344
14.2.1.2
System of material points constrained by more
equations
................................ 346
14.3
Demonstration of the virtual velocity principle
................ 348
15
Complementary virtual work laws
............................. 353
15.1
Augustin Cauchy
formulation
.............................. 354
15.1.1
Kinematics of plane rigid bodies
.................... 356
16
The treatises of mechanics
.................................... 361
16.1
Simeon Denis
Poisson
.................................... 362
16.2
Jean Marie
Duhamel
..................................... 365
16.3
Gaspard Gustave Coriolis
................................. 367
17
Virtual work laws and continuum mechanics
.................... 375
17.1
First applications
....................................----- 375
17.1.
1 Joseph Louis
Lagrange.........,.................. 375
17.1.1.1
Mono-dimensional continuum
.............. 376
17.
і
. 1.2
Three-dimensional continuum
......-----.... 377
17.1.2
Navieťs
équations
of motion
...................... · 381
1
7.2
Applications in the theory of elasticity
...................... 383
xii Contents
17.2.1 Alfred Clebsch................................... 383
17.3
The Italian school........................................
387
17.3.1 Gabrio
Piola
..................................... 388
17.3.2
Eugenio
Belframi
................................. 390
17.3.3 Enrico
Betti
..................................... 392
18
Thermodynamical approach ..................................
395
18.1
Pierre Duhem s concept of
oeuvre
.......................... 396
18.1.1
Virtual transformations
............................ 397
18.1.2
Activity, energy and work
......................... 398
18.1.3
Rational mechanics
............................... 401
18.1.3.1
Free systems
............................. 401
18.1.3.2
Constrained systems
...................... 402
Appendix. Quotations
............................................. 405
A.I Chapter
1............................................... 405
A.2 Chapter
2............................................... 406
A.3 Chapter
3............................................... 407
A.4 Chapter
4............................................... 409
A.5 Chapter
5............................................... 412
A.6
Chapter6
............................................... 423
A.7 Chapter
7............................................... 426
A.8 Chapter
8............................................... 433
A.9 Chapter
9............................................... 437
АЛО
Chapter
10.............................................. 441
A.I
1
Chapter
11.............................................. 448
A.12 Chapter
12.............................................. 452
A.13 Chapter
13.............................................. 454
A.14 Chapter
14.............................................. 457
A.15 Chapter
15.............................................. 463
A.16 Chapter
16.............................................. 464
A.17 Chapter
17.............................................. 467
A.18 Chapter
18.............................................. 471
References
....................................................... 473
Index
........................................................... 489
|
| any_adam_object | 1 |
| author | Capecchi, Danilo |
| author_facet | Capecchi, Danilo |
| author_role | aut |
| author_sort | Capecchi, Danilo |
| author_variant | d c dc |
| building | Verbundindex |
| bvnumber | BV039953497 |
| classification_rvk | CC 3500 UB 2405 |
| ctrlnum | (OCoLC)785512630 (DE-599)BVBBV039953497 |
| dewey-full | 530.474 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.474 |
| dewey-search | 530.474 |
| dewey-sort | 3530.474 |
| dewey-tens | 530 - Physics |
| discipline | Physik Philosophie |
| era | Geschichte 350 v. Chr.-1910 gnd Geschichte 350 v. Chr.-2010 gnd |
| era_facet | Geschichte 350 v. Chr.-1910 Geschichte 350 v. Chr.-2010 |
| format | Book |
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| id | DE-604.BV039953497 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:06:02Z |
| institution | BVB |
| isbn | 9788847020559 9788847020016 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024811390 |
| oclc_num | 785512630 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-12 DE-11 DE-188 DE-210 DE-703 |
| owner_facet | DE-355 DE-BY-UBR DE-12 DE-11 DE-188 DE-210 DE-703 |
| physical | XII, 492 S. Ill., graph. Darst. 24 cm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Science networks, historical studies |
| series2 | Science networks, historical studies |
| spellingShingle | Capecchi, Danilo History of virtual work laws a history of mechanics prospective Science networks, historical studies Mechanik (DE-588)4038168-7 gnd |
| subject_GND | (DE-588)4038168-7 |
| title | History of virtual work laws a history of mechanics prospective |
| title_auth | History of virtual work laws a history of mechanics prospective |
| title_exact_search | History of virtual work laws a history of mechanics prospective |
| title_full | History of virtual work laws a history of mechanics prospective Danilo Capecchi |
| title_fullStr | History of virtual work laws a history of mechanics prospective Danilo Capecchi |
| title_full_unstemmed | History of virtual work laws a history of mechanics prospective Danilo Capecchi |
| title_short | History of virtual work laws |
| title_sort | history of virtual work laws a history of mechanics prospective |
| title_sub | a history of mechanics prospective |
| topic | Mechanik (DE-588)4038168-7 gnd |
| topic_facet | Mechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024811390&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002495563 |
| work_keys_str_mv | AT capecchidanilo historyofvirtualworklawsahistoryofmechanicsprospective |