エラスティカを巡る数理 : ベルヌイ,オイラーから現代まで

書誌事項

タイトル別名
  • Mathematics in Elastica : From the Studies of Bernoulli and Euler to Current Ones

抄録

In 1691, James Bernoulli proposed the following problem called elastica problem : "What shape of elastica, an ideal thin elastic rod in a plane, is allowed ?" Euler essentially solved the problem in 1744 by developing studies of variation problem and elliptic function theory. Their studies are regarded as prototypes of harmonic map theory, nonlinear differential theory, soliton theory, differential geometry, algebraic geometry, theory of moduil of elliptic curves and so on. In this article we mention their mathematical meaning with their historical background from viewpoint of pure and applied mathematics : Their studies started from concreteness to abstractand they applied constructed abstract theory to the concrete problem. We also introduce a current study of statistical mechanics of elasticas, which might be settled by knowledge of hyperelliptic function theory.

収録刊行物

  • 応用数理

    応用数理 13 (1), 48-60, 2003

    一般社団法人 日本応用数理学会

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詳細情報

  • CRID
    1390001205765185920
  • NII論文ID
    110001888829
  • DOI
    10.11540/bjsiam.13.1_48
  • ISSN
    24321982
  • 本文言語コード
    ja
  • データソース種別
    • JaLC
    • CiNii Articles
  • 抄録ライセンスフラグ
    使用不可

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