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Historical Studies on the systematization of classical mechanics in the 18^<th> century

Research Project

Project/Area Number 14580004
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 科学技術史(含科学社会学・科学技術基礎論)
Research InstitutionKyoto University

Principal Investigator

ITO Kazuyuki  Kyoto University, Graduate School of Letters, Associate Professor, 大学院・文学研究科, 助教授 (60273421)

Co-Investigator(Kenkyū-buntansha) 中田 良一  金蘭短期大学, 教養教育科, 教授 (50164215)
Project Period (FY) 2002 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2005: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2004: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2003: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2002: ¥2,000,000 (Direct Cost: ¥2,000,000)
Keywordshistory of science / classical mechanics / Euler / equation of motion / laws of motion / d'Alembert / Lagrange / 18世紀科学 / 剛体の運動 / 剛体の回転運動 / 角運動量
Research Abstract

Classical mechanics is generally regarded as having been founded by Isaac Newton in the late 17th century, but his mathematical arguments in Principia are geometrical and very different from those of ours. In this study, we discuss the process of constructing the analytic and systematic system of classical mechanics in the 18th century, particularly the mechanical theory of Leonhard Euler who played the principal role in this process.
Euler firstly used the systematic method of setting the coordinate axes fixed in space and deriving the equation of motion as the second-differential equation for each coordinate. From it, he also the conservation laws of "vis viva" (kinetic energy), linear momentum and angular momentum. Further he extended the object of his method from mass points to rigid bodies, and derived the so-called Euler equation of rigid bodies.
This transition of mechanics to new one founded on the analytical calculus happed in the second part of 1740s by Euler's study of motion of planets and rigid bodies. It is very important that in this period the mathematical formula of Euler's equation of motion has changed largely.
In his younger period, he derived the equation of motion from Galileo's law of free fall, and it had the particular formula of the first-order differential equation of space. Later, its formula has changed to the second-order differential equation of coordinate and the influence of Galileo's law has decreased, but we can distinguish its influence in the factor 2 of his equation of motion and his unit system of mechanics.

Report

(5 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (15 results)

All 2006 2004 2003 Other

All Journal Article (11 results) Publications (4 results)

  • [Journal Article] オイラーの運動方程式2006

    • Author(s)
      伊藤 和行
    • Journal Title

      科学哲学科学史研究 1号

      Pages: 153-169

    • NAID

      120000890681

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Euler's Equation of Motion2006

    • Author(s)
      Kazuyuki ITO
    • Journal Title

      Philosophy and History of Science Studies No.1

      Pages: 153-169

    • NAID

      120000890681

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] オイラーの運動方程式2006

    • Author(s)
      伊藤 和行
    • Journal Title

      科学哲学科学史研究 1

      Pages: 153-169

    • NAID

      120000890681

    • Related Report
      2005 Annual Research Report
  • [Journal Article] 落下法則-古典力学の誕生と数学2004

    • Author(s)
      伊藤 和行
    • Journal Title

      人文知の新たな総合に向けて

      Pages: 45-53

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Law of Falling Motion : Birth of Classical Mechanics and Mathematics2004

    • Author(s)
      Kazuyuki ITO
    • Journal Title

      Towards New Integration of Human Knowledge, Graduate School of Letters, Kyoto University

      Pages: 45-553

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] 落下法則-古典力学の誕生と数学-2004

    • Author(s)
      伊藤和行
    • Journal Title

      人文知の新たな総合へ向けて

      Pages: 45-53

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Leonhard Eulerによる古典力学の解析化2004

    • Author(s)
      中田良一
    • Journal Title

      人文知の新たな総合へ向けて

      Pages: 55-66

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Concept of Force in Jean le Rondd'Alembert2004

    • Author(s)
      Ryoichi Nakata
    • Journal Title

      千里金蘭大学短期大学部紀要 34

      Pages: 53-75

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Some Remarks on Alexis Fontaine's Mechanics2004

    • Author(s)
      Ryoichi Nakata
    • Journal Title

      千里金蘭大学短期大学部紀要 34

      Pages: 39-52

    • Related Report
      2004 Annual Research Report
  • [Journal Article] 斜面運動の「原理」-機械学から運動論へ-2003

    • Author(s)
      伊藤 和行
    • Journal Title

      科学史研究 228号

      Pages: 233-235

    • NAID

      10024229803

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The <Principle> of Falling Motion on Inclined Planes : from Mechanics to Science of Motion2003

    • Author(s)
      Kazuyuki ITO
    • Journal Title

      Japanese Studies in History of Science No.228

      Pages: 233-235

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Publications] 伊藤 和行: "斜面運動の「原理」-機械学から運動論へ-"科学史研究. 42・228. 233-235 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Ryoichi Nakata: "Discussion of the precession of the equinexes of the Earth by Euter"W.Schroder ed., Meteorological and Geophxsical Fluid Dynamics. 147-160 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 中田良一: "Johann BernoulliとDaniel Bernoulliの回転する管の中の運動に関する解析"金蘭短期大学研究誌. 33. 61-81 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Ryoichi Nakata: "The General Principles of Resolving Mechanical Problems ind' Alembert Clairant and Euler"Historia Scientiarum. 12. 18-42 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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