Huygens and Barrow, Newton and Hooke: Pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals

Portada
Birkhäuser, 6 de des. 2012 - 118 pàgines

Translated from the Russian by E.J.F. Primrose
"Remarkable little book." -SIAM REVIEW
V.I. Arnold, who is renowned for his lively style, retraces the beginnings of mathematical analysis and theoretical physics in the works (and the intrigues!) of the great scientists of the 17th century.
Some of Huygens' and Newton's ideas. several centuries ahead of their time, were developed only recently. The author follows the link between their inception and the breakthroughs in contemporary mathematics and physics.
The book provides present-day generalizations of Newton's theorems on the elliptical shape of orbits and on the transcendence of abelian integrals; it offers a brief review of the theory of regular and chaotic movement in celestial mechanics, including the problem of ports in the distribution of smaller planets and a discussion of the structure of planetary rings.

 

Pàgines seleccionades

Continguts

Huygens and Barrow Newton and Hooke
8
Chapter
11
The problem of falling bodies
16
Celestial mechanics 17 Newton after the Principia
17
18 The natural philosophy of Newton
18
19 The triumphs of celestial mechanics
19
20 Laplaces theorem on stability
20
21 Will the Moon fall to Earth?
21
Did Newton prove that orbits are elliptic?
30
31 Newtons proof and modern mathematics
31
Chapter 2
35
The Newton polygon
36
Barrow
38
10 Taylor series
42
11 Leibniz
44
12 Discussion on the invention of analysis
49

The inverse square law
22
23 The TitiusBode law and the minor planets
23
The Principia
24
Keplers second law and the topology of Abelian integrals 25 Newtons theorem on the transcendence of integrals
25
Attraction of spheres
26
27 Newtons theorem on local nonalgebraicity
27
28 Analyticity of smooth algebraic curves
28
29 Algebraicity of locally algebraically integrable ovals
29
Chapter 3
53
14 The wave fronts of Huygens
56
15 Evolvents and the icosahedron
58
16 The icosahedron and quasicrystals
62
Appendix 1
95
of Newtons Principia
101
Notes
107
Copyright

Altres edicions - Mostra-ho tot

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Frases i termes més freqüents

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Informació bibliogràfica

TítolHuygens and Barrow, Newton and Hooke: Pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals
AutorVladimir I. Arnold
Edicióil·lustrada
EditorBirkhäuser, 2012
ISBN3034891296, 9783034891295
Nre. de pàgines118 pàgines
  
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