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AuthorSchulze, Thorsten. author
TitleHuygens and Barrow, Newton and Hooke [electronic resource] : Pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals / by V. I. Arnol'd
ImprintBasel : Birkhรคuser Basel, 1990
Connect tohttp://dx.doi.org/10.1007/978-3-0348-9129-5
Descript 118 p. 1 illus. online resource

SUMMARY

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


CONTENT

Huygens and Barrow, Newton and Hooke -- 1. The law of universal gravitation -- ยง 1. Newton and Hooke -- ยง 2. The problem of falling bodies -- ยง 3. The inverse square law -- ยง 4. The Principia -- ยง 5. Attraction of spheres -- ยง 6. Did Newton prove that orbits are elliptic? -- 2. Mathematical analysis -- ยง 7. Analysis by means of power series -- ยง 8. The Newton polygon -- ยง 9. Barrow -- ยง10. Taylor series -- ยง11. Leibniz -- ยง12. Discussion on the invention of analysis -- 3. From evolvents to quasicrystals -- ยง13. The evolvents of Huygens -- ยง14. The wave fronts of Huygens -- ยง15. Evolvents and the icosahedron -- ยง16. The icosahedron and quasicrystals -- 4. Celestial mechanics -- ยง17. Newton after the Principia -- ยง18. The natural philosophy of Newton -- ยง19. The triumphs of celestial mechanics -- ยง20. Laplace's theorem on stability -- ยง21. Will the Moon fall to Earth? -- ยง22. The three body problem -- ยง23. The Titius-Bode law and the minor planets -- ยง24. Gaps and resonances -- 5. Kepler's second law and the topology of Abelian integrals -- ยง25. Newton's theorem on the transcendence of integrals -- ยง26. Local and global algebraicity -- ยง27. Newton's theorem on local non-algebraicity -- ยง28. Analyticity of smooth algebraic curves -- ยง29. Algebraicity of locally algebraically integrable ovals -- ยง30. Algebraically non-integrable curves with singularities -- ยง31. Newton's proof and modern mathematics -- Appendix 1. Proof that orbits are elliptic -- Appendix 2. Lemma XXVIII of Newton's Principia -- Notes


Mathematics Mathematical analysis Analysis (Mathematics) Mathematics Analysis



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