Dynamical Systems X: General Theory of Vortices

Front Cover
Springer Science & Business Media, May 12, 2003 - Science - 184 pages
0 Reviews
The English teach mechanics as an experimental science, while on the Continent, it has always been considered a more deductive and a priori science. Unquestionably, the English are right. * H. Poincare, Science and Hypothesis Descartes, Leibnitz, and Newton As is well known, the basic principles of dynamics were stated by New ton in his famous work Philosophiae Naturalis Principia Mathematica, whose publication in 1687 was paid for by his friend, the astronomer Halley. In essence, this book was written with a single purpose: to prove the equivalence of Kepler's laws and the assumption, suggested to Newton by Hooke, that the acceleration of a planet is directed toward the center of the Sun and decreases in inverse proportion to the square of the distance between the planet and the Sun. For this, Newton needed to systematize the principles of dynamics (which is how Newton's famous laws appeared) and to state the "theory of fluxes" (analysis of functions of one variable). The principle of the equality of an action and a counteraction and the inverse square law led Newton to the theory of gravitation, the interaction at a distance. In addition, New ton discussed a large number of problems in mechanics and mathematics in his book, such as the laws of similarity, the theory of impact, special vari ational problems, and algebraicity conditions for Abelian integrals. Almost everything in the Principia subsequently became classic. In this connection, A. N.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

VII
9
VIII
16
IX
23
X
29
XI
37
XII
46
XIII
52
XIV
61
XXIII
114
XXIV
120
XXV
125
XXVI
129
XXVII
135
XXVIII
139
XXIX
143
XXX
152

XV
70
XVI
76
XVII
80
XVIII
87
XIX
90
XX
97
XXI
101
XXII
108
XXXI
157
XXXII
160
XXXIII
165
XXXIV
169
XXXV
177
XXXVI
181
Copyright

Common terms and phrases

Popular passages

Page 179 - Morse-Sard theorem for real-analytic functions. Theory Nonlin. Operators. Proc. Summer School, Babylon 1971, 121-125.

References to this book

All Book Search results »

Bibliographic information