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A Study of Analysis and Design of Complex Multibody Systems by the Implcit Lagrangian Method

Research Project

Project/Area Number 23560269
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Dynamics/Control
Research InstitutionWaseda University

Principal Investigator

YOSHIMURA HIROAKI  早稲田大学, 理工学術院, 教授 (40247234)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2011: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Keywords陰的なラグランジュ系 / ディラック構造 / シンプレクティック構造 / マルチボディシステム / ネットワーク構造 / ラグランジュ・ダランベール原理 / ハミルトン・ポントリヤーギン原理 / スパースタブロー法 / シンプレティック構造 / 国際研究者交流
Research Abstract

The purpose of this research is to develop a systematic method of analysis and design for complex multibody systems such as artificial satellite, robots, electric circuits and so on by the theory of implicit Lagrangian systems, which enables us to treat mechanical systems with nonholonomic constraints as well as with Dirac constraints. In this study, we have principally investigated the following items:(1) Decomposition into subsystems and interconnection for structuring systems, (2) Dynamical formalism for moduled implicit Lagrangian systems, (3) Development of discrete Lagrange-d'Alembert principle for structure preserving a numerical integration scheme. Finally, we have shown the validity of the proposed method by some illustrative examples of nonlinear L-C circuits, robots, nonholonomic mechanical systems and space mission design.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (53 results)

All 2014 2013 2012 2011 Other

All Journal Article (15 results) (of which Peer Reviewed: 14 results) Presentation (37 results) (of which Invited: 6 results) Remarks (1 results)

  • [Journal Article] Tensor Products of Dirac Structures and Interconnection in Lagrangian Mechanics2014

    • Author(s)
      Henry Jacobs and Hiroaki Yoshimura
    • Journal Title

      Journal of Geometric Mechanics

      Volume: Vol.6, No.1 Pages: 67-98

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Invariant Manifolds and Lagrangian Coherent Structures in the Planar Circular Restricted Three-Body Problem2014

    • Author(s)
      Kaori Onozaki and Hiroaki Yoshimura
    • Journal Title

      Proceeding of NCTAM,Theoretical and Applied Mechanics Japan

      Volume: vol.62 Pages: 119-128

    • NAID

      130004463857

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] 平面楕円制限3体問題における月への輸送軌道の設計2014

    • Author(s)
      小野崎香織,吉村浩明
    • Journal Title

      システム制御情報学会論文誌

      Volume: Vol.27,No.4 Pages: 160-165

    • NAID

      130004565054

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Dirac Reduction of binary asteroid systems with symmetry and stability of relative equilibria2013

    • Author(s)
      Kaori Onozaki and Hiroaki Yoshimura
    • Journal Title

      Theoretical & Applied Mechanics Letters

      Volume: 3 Pages: 130111-130118

    • Related Report
      2013 Annual Research Report 2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] A graph-theoretic approach to sparse matrix inversion for implicit differential algebraic equations2013

    • Author(s)
      Hiroaki Yoshimura
    • Journal Title

      Mech. Sci.

      Volume: 4 Pages: 243-250

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lunar Capture Trajectories in the Four-Body Problem2013

    • Author(s)
      Kaori Onozaki and Hiroaki Yoshimura
    • Journal Title

      Proc. Of AIAA SPACE 2013 Conference and Exposition

      Volume: (Chapter) Pages: 1-6

    • DOI

      10.2514/6.2013-5425

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Hamilton-Pontryagin Principle and Multi-Dirac Structures for Classical Field Theories2012

    • Author(s)
      Joris Vankerschaver, Hiroaki Yoshimura and Melvin Leok
    • Journal Title

      Journal of Mathematical Physics

      Volume: 53 Pages: 72903-72903

    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] ディラック構造のテンソル積と力学への応用2012

    • Author(s)
      吉村浩明
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 第1774巻 Pages: 21-34

    • Related Report
      2013 Final Research Report 2011 Research-status Report
  • [Journal Article] Tensor Products of Dirac Structures and Interconnection of Implicit Lagrangian Systems2012

    • Author(s)
      Hiroaki Yoshimura and Henry Jacobs
    • Journal Title

      Proc. of 20th International Symposium on Mathematical Theory of Networks and Systems

      Volume: MTNS2012_0288 Pages: 8-8

    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Dirac Reduction of Binary Asteroid Systems with Symmetry and Stability of Relative Equilibria2012

    • Author(s)
      Kaori Onozaki and Hiroaki Yoshimura
    • Journal Title

      The 6th Asian Conference on Multibody Dynamics

      Volume: Vol.6, No.12300 Pages: 1-8

    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the Geometry of Multi-Dirac Structures and Gerstenhaber Algebras2011

    • Author(s)
      Joris Vankerschaver, Hiroaki Yoshimura and Melvin Leok
    • Journal Title

      Journal of Geometry and Physics

      Volume: 61 Pages: 1415-1425

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Nonlinear Phenomena in Rayleigh-Plesset Equation for Single Bubble Dynamics2011

    • Author(s)
      Shohei Shikada and Hiroaki Yoshimura
    • Journal Title

      Proceedings of the Sixth International Conference on Fluid Mechanics, American Institute of Physics Conf.

      Volume: 1376 Pages: 552-554

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Hamilton-Pontryagin Principle for Incompressible Ideal Fluids2011

    • Author(s)
      Francois Gay-Balmaz and Hiroaki Yoshimura
    • Journal Title

      Proceedings of the Sixth International Conference on Fluid Mechanics American Institute of Physics Conf.

      Volume: 1376 Pages: 645-647

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Interconnection and Composition of Dirac Structures for Lagrange-Dirac Systems2011

    • Author(s)
      Henry Jacobs and Hiroaki Yoshimura
    • Journal Title

      Proc. 50th IEEE Conference on Decision and Control

      Volume: 1 Pages: 1-6

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Tensor Products of Dirac Structures and Interconnection of Implicit Lagrangian Systems

    • Author(s)
      Hiroaki Yoshimura and Henry Jacobs
    • Journal Title

      Proc. of 20^<th> International Symposium on Mathematical Theory of Networks and Systems 2012

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Presentation] Discrete Lagrangian Systems and Variational Integrators for Interconnected Systems2014

    • Author(s)
      Hiroaki Yoshimura
    • Organizer
      Geometry and Physics XII -- Geometric Mechanics
    • Place of Presentation
      Sanya in China
    • Year and Date
      2014-03-12
    • Related Report
      2013 Final Research Report
  • [Presentation] 制限3体問題に基づく宇宙機のミッションと月への輸送軌道の設計2013

    • Author(s)
      小野崎香織,吉村浩明
    • Organizer
      力学系理論の応用に関する研究会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2013-03-26
    • Related Report
      2013 Final Research Report
  • [Presentation] The Hamilton-Pontryagin Principle and Lie-Dirac Reduction with Advective Parameters2013

    • Author(s)
      Hiroaki Yoshimura and Francois Gay-Balmaz
    • Organizer
      SIAM Conference on Dynamical Systems
    • Place of Presentation
      Snowbird
    • Related Report
      2013 Final Research Report
  • [Presentation] Lunar Capture Trajectories in the Coupled Restricted Three-Body Problem2013

    • Author(s)
      Kaori Onozaki and Hiroaki Yoshimura
    • Organizer
      Taiwan-Japan Symposium on Celestial Mechanics and N-Body Dynamics
    • Place of Presentation
      Taiwan National Tsing Hua University
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Presentation] Variational Integrators and Discrete Lagrangian Mechanics for Interconnected Systems2013

    • Author(s)
      Hiroaki Yoshimura and Satoshi Hanawa
    • Organizer
      Scientific Computation and Differential Equations
    • Place of Presentation
      Valladolid
    • Related Report
      2013 Final Research Report
  • [Presentation] 制限三体問題におけるFTLEと不変多様体の解析2013

    • Author(s)
      小野崎香織,堀恭暢,吉村浩明
    • Organizer
      第62回理論応用力学講演会講演論文集
    • Place of Presentation
      東京工業大学
    • Related Report
      2013 Final Research Report
  • [Presentation] 楕円制限三体問題における月への輸送軌道の設計2013

    • Author(s)
      小野崎香織,吉村浩明
    • Organizer
      第57回システム制御情報学会研究発表講演会講演論文集
    • Place of Presentation
      兵庫県民会館
    • Related Report
      2013 Final Research Report
  • [Presentation] 倒立二輪移動ロボットの非ホロノミック軌道制御2013

    • Author(s)
      藤掛俊多,山田修平,吉村浩明
    • Organizer
      日本機械学会第22回交通物流部門講演会
    • Place of Presentation
      東京大学
    • Related Report
      2013 Final Research Report
  • [Presentation] The Hamilton-Pontryagin Principle and Lie-Dirac Reduction with Advective Parameters2013

    • Author(s)
      Hiroaki Yoshimura and Francois Gay-Balmaz
    • Organizer
      SIAM Conference on Dynamical Systems
    • Place of Presentation
      Snowbird, USA
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Variational Integrators and Discrete Lagrangian Mechanics for Interconnected Systems2013

    • Author(s)
      Hiroaki Yoshimura and Satoshi Hanawa
    • Organizer
      Scientific Computation and Differential Equations
    • Place of Presentation
      Valladolid
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 楕円制限三体問題における月への輸送軌道の設計2013

    • Author(s)
      小野崎 香織, 吉村 浩明
    • Organizer
      第57回システム制御情報学会研究発表講演会
    • Place of Presentation
      兵庫県民会館
    • Related Report
      2013 Annual Research Report
  • [Presentation] 倒立二輪移動ロボットの非ホロノミック軌道制御2013

    • Author(s)
      藤掛俊多,山田修平,吉村浩明
    • Organizer
      日本機械学会第22回交通物流部門講演会
    • Place of Presentation
      東京大学生産技術研究所
    • Related Report
      2013 Annual Research Report
  • [Presentation] Dirac Structures in Vakonomic Mechanics2013

    • Author(s)
      Hiroaki Yoshimura
    • Organizer
      IRSES Meeting on Differential Geometry and Mechanics
    • Place of Presentation
      Ghent University
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] 陰的なラグランジュ系による拘束力学系の定式化とDAEの数値解析2012

    • Author(s)
      吉村浩明
    • Organizer
      計測自動制御学会,2012年度第2回プラントモデリング部会研究会
    • Place of Presentation
      サイバネットシステム本社,東京
    • Year and Date
      2012-12-03
    • Related Report
      2013 Final Research Report
  • [Presentation] Dirac Structures, Variational Principles and Reduction in Mechanics, Conference on Geometry2012

    • Author(s)
      Hiroaki Yoshimura
    • Organizer
      Symmetry, Dynamics, and Control : The Legacy of Jerry Marsden, Fields Institute
    • Place of Presentation
      University of Toronto
    • Year and Date
      2012-07-27
    • Related Report
      2013 Final Research Report
  • [Presentation] Lie-Dirac Reduction and Applications to Mechanics2012

    • Author(s)
      Hiroaki Yoshimura
    • Organizer
      Seminar of Poisson Geometry
    • Place of Presentation
      Keio University
    • Year and Date
      2012-03-05
    • Related Report
      2013 Final Research Report
  • [Presentation] Dirac Structures in Vakonomic Mechanics2012

    • Author(s)
      Hiroaki Yoshimura
    • Organizer
      IRES Meeting on Differential Geometry and Mechanics
    • Place of Presentation
      Ghent University
    • Year and Date
      2012-01-16
    • Related Report
      2013 Final Research Report
  • [Presentation] 陰的なラグランジュ系による柔軟多体系のダイナミクスの定式化2012

    • Author(s)
      長谷龍一,田川悟,吉村浩明
    • Organizer
      日本機械学会,機械力学・計測制御部門Dynamics and Design Conference 2012講演論文集
    • Place of Presentation
      慶応義塾大学
    • Related Report
      2013 Final Research Report
  • [Presentation] 剛体で構成された小惑星ペアの相対平衡と安定性2012

    • Author(s)
      小野崎香織,吉村浩明
    • Organizer
      日本機械学会2012年度年次大会
    • Place of Presentation
      金沢大学
    • Related Report
      2013 Final Research Report
  • [Presentation] ホロノミック拘束を受けるラグランジュ系の幾何学的安定化法2012

    • Author(s)
      塙智史,吉村浩明
    • Organizer
      第55回自動制御連合講演会
    • Place of Presentation
      京都大学
    • Related Report
      2013 Final Research Report
  • [Presentation] Tensor Products of Dirac Structures and Interconnection of Implicit Lagrangian Systems2012

    • Author(s)
      Hiroaki Yoshimura and Henry Jacobs
    • Organizer
      20th International Symposium on Mathematical Theory of Networks and Systems
    • Place of Presentation
      University of Melbourne
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Dirac Structures, Variational Principles and Reduction in Mechanics –Toward Understanding Interconnection Structures in Physical Systems- Conference on Geometry2012

    • Author(s)
      Hiroaki Yoshimura
    • Organizer
      Conference on Geometry, Symmetry, Dynamics, and Control: The Legacy of Jerry Marsden
    • Place of Presentation
      Fields Institute, University of Toronto
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Dirac Reduction of Binary Asteroid Systems with Symmetry and Stability of Relative Equilibria2012

    • Author(s)
      Kaori Onozaki and Hiroaki Yoshimura
    • Organizer
      The 6th Asian Conference on Multibody Dynamics
    • Place of Presentation
      Shanghai, Jiotong University, China
    • Related Report
      2012 Research-status Report
  • [Presentation] 制限三体問題におけるFTLEによる不変多様体の解析, 第 62 回理論応用力学講演会2012

    • Author(s)
      小野崎香織,堀 恭暢, 吉村浩明
    • Organizer
      第 62 回理論応用力学講演会
    • Place of Presentation
      東京工業大学 大岡山キャンパス
    • Related Report
      2012 Research-status Report
  • [Presentation] 剛体で構成された小惑星ペアの相対平衡と安定性2012

    • Author(s)
      小野崎香織,吉村浩明
    • Organizer
      日本機械学会2012年度年次大会
    • Place of Presentation
      金沢大学 角間キャンパス
    • Related Report
      2012 Research-status Report
  • [Presentation] レイリー・ベナール対流とラグランジュ・コヒーレント構造2012

    • Author(s)
      菅原拓也,吉村浩明
    • Organizer
      日本機械学会 2012年度年次大会
    • Place of Presentation
      金沢大学 角間キャンパス
    • Related Report
      2012 Research-status Report
  • [Presentation] レイリー・ベナール対流に現れるラグランジュ・コヒーレント構造とカオス2012

    • Author(s)
      菅原拓也,吉村浩明
    • Organizer
      日本流体力学会 2012年度年次大会
    • Place of Presentation
      高知大学 朝倉キャンパス
    • Related Report
      2012 Research-status Report
  • [Presentation] 陰的なラグランジュ系による柔軟多体系のダイナミクスの定式化2012

    • Author(s)
      長谷龍一,田川悟,吉村浩明
    • Organizer
      日本機械学会,機械力学・計測制御部門 Dynamics and Design Conference 2012
    • Place of Presentation
      慶應大学 日吉キャンパス
    • Related Report
      2012 Research-status Report
  • [Presentation] ホロノミック拘束を受けるラグランジュ系の幾何学的安定化法2012

    • Author(s)
      塙 智史,吉村 浩明
    • Organizer
      第55回自動制御連合講演会
    • Place of Presentation
      京都大学 吉田キャンパス
    • Related Report
      2012 Research-status Report
  • [Presentation] 非圧縮性流体の変分原理を用いた定式化と粒子法による流体解析2012

    • Author(s)
      宮本卓哉, 吉村浩明
    • Organizer
      日本応用数理学会 2012年度年会
    • Place of Presentation
      稚内,全日空ホテル
    • Related Report
      2012 Research-status Report
  • [Presentation] Lie-Dirac Reduction and Applications to Mechanics2012

    • Author(s)
      Hiroaki Yoshimura
    • Organizer
      Seminar of Poisson Geometry(招待講演)
    • Place of Presentation
      慶応義塾大学
    • Related Report
      2011 Research-status Report
  • [Presentation] レイリー・プレセット方程式による単一気泡の非線形挙動と分岐2011

    • Author(s)
      吉村浩明,鹿田翔平,仲原慎一郎
    • Organizer
      日本機械学会第3 回マイクロ・ナノ工学シンポジウム
    • Place of Presentation
      タワーホール船堀
    • Related Report
      2011 Research-status Report
  • [Presentation] 分子動力学法による単一気泡の生成と崩壊挙動の解析2011

    • Author(s)
      鷲頭亮介,吉村浩明
    • Organizer
      日本機械学会第3 回マイクロ・ナノ工学シンポジウム
    • Place of Presentation
      タワーホール船堀
    • Related Report
      2011 Research-status Report
  • [Presentation] ディラック構造の相互接続とその応用2011

    • Author(s)
      吉村浩明
    • Organizer
      京都大学数理解析研究所研究集会「幾何学的力学系の新展開」
    • Place of Presentation
      京都大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Interconnection, Dirac Structures and Dirac Systems in Mechanics2011

    • Author(s)
      Hiroaki Yoshimura
    • Organizer
      The Oberwolfach Workshop Applied Dynamics and Geometric Mechanics(招待講演)
    • Place of Presentation
      Oberwolfach
    • Related Report
      2011 Research-status Report
  • [Presentation] Lie-Dirac Reduction and Applications to Mechanics

    • Author(s)
      Hiroaki Yoshimura
    • Organizer
      Seminar of Poisson Geometry
    • Place of Presentation
      Keio University, Yagami Campus
    • Related Report
      2012 Research-status Report
  • [Presentation] 陰的なラグランジュ系による拘束力学系の定式化とDAEの数値解析

    • Author(s)
      吉村浩明
    • Organizer
      計測自動制御学会,2012年度 第2回プラントモデリング部会研究会
    • Place of Presentation
      サイバネットシステム本社
    • Related Report
      2012 Research-status Report
    • Invited
  • [Remarks]

    • URL

      http://www.yoshimura.mech.waseda.ac.jp/

    • Related Report
      2013 Final Research Report

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

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