© 2011

Flexible Multibody Dynamics


Part of the Solid Mechanics and Its Applications book series (SMIA, volume 176)

Table of contents

  1. Front Matter
    Pages 1-20
  2. Basic tools and concepts

    1. Front Matter
      Pages 1-1
    2. O. A. Bauchau
      Pages 3-29
    3. O. A. Bauchau
      Pages 31-55
    4. O. A. Bauchau
      Pages 57-105
    5. O. A. Bauchau
      Pages 107-157
  3. Rigid body dynamics

    1. Front Matter
      Pages 159-159
    2. O. A. Bauchau
      Pages 161-200
    3. O. A. Bauchau
      Pages 201-250
  4. Concepts of analytical dynamics

    1. Front Matter
      Pages 251-251
    2. O. A. Bauchau
      Pages 253-294
    3. O. A. Bauchau
      Pages 295-347
  5. Constrained dynamical systems

    1. Front Matter
      Pages 349-349
    2. O. A. Bauchau
      Pages 351-384
    3. O. A. Bauchau
      Pages 385-424
    4. O. A. Bauchau
      Pages 425-461
    5. O. A. Bauchau
      Pages 463-507
  6. Parameterization of rotation and motion

    1. Front Matter
      Pages 509-509
    2. O. A. Bauchau
      Pages 511-542
    3. O. A. Bauchau
      Pages 543-565

About this book


The author developed this text over many years, teaching graduate courses in advanced dynamics and flexible multibody dynamics at the Daniel Guggenheim School of Aerospace Engineering of the Georgia Institute of Technology.


The book presents a unified treatment of rigid body dynamics, analytical dynamics, constrained dynamics, and flexible multibody dynamics. A comprehensive review of numerical tools used to enforce both holonomic and nonholonomic constraints is presented. Advanced topics such as Maggi’s, index-1, null space, and Udwadia and Kalaba’s formulations are presented because of their fundamental importance in multibody dynamics. Methodologies for the parameterization of rotation and motion are discussed and contrasted. Geometrically exact beams and shells formulations, which have become the standard in flexible multibody dynamics, are presented and numerical aspects of their finite element implementation detailed. Methodologies for the direct solution of the index-3 differential-algebraic equations characteristic of constrained multibody systems are presented. It is shown that with the help of proper scaling procedures, such equations are not more difficult to integrate than ordinary differential equations.


This book is illustrated with numerous examples and should prove valuable to both students and researchers in the fields of rigid and flexible multibody dynamics.


multibody dynamics

Authors and affiliations

  1. 1.School of Aerospace EngineeringGeorgia Institute of TechnologyAtlantaUSA

About the authors

Olivier Bauchau teaches and conducts research in the fields of structural dynamics, multibody dynamics, experimental dynamics, and mechanics of advanced composite materials and structures. He was educated at Université de l'Etat à Liège (Belgium), Massachusetts Institute of Technology, Cambridge, MA. He has worked as a researcher at St. Gobain Récherches in Paris, France and as associate professor at the department of Mechanical Engineering, Aeronautical Engineering, and Mechanics at the Rensselaer Polytechnic Institute in Troy, NY, before settling as a professor at the Daniel Guggenheim School of Aerospace Engineering, at the Georgia Institute of Technology in Atlanta, Georgia. Faculty responsibilities include teaching of graduate and undergraduate courses, and conducting research in the fields of structural dynamics, multibody dynamics, experimental dynamics, and mechanics of advanced composite materials and structures.

Professor Bauchau is an Engineering Consultant with United Technologies Research Center in Hartford, CT.; Sikorsky Aircraft in Stratford, CT.;  Bell Helicopter in Fort Worth, TX.; NASA Ames Research Center in Moffet Field, CA; NASA Langley Research Center in Hampton, VA; Advanced Rotorcraft Technology Inc. in Mountain View, CA.; Materials Technologies Corporation in Monroe, CT.

His fields of expertise include teaching undergraduate and graduate courses in the areas of Theory of Structures, Strength of Materials, Advanced Structural Analysis, Design with Composite Materials, Aeroelasticity, Finite Element Methodologies, Engineering Mechanics, Structural Dynamics, Machine Dynamics, and Engineering Laboratories, as well as conducting research in the areas of Finite Element Methods for Structural and Multibody Dynamics, Experimental Mechanics and Dynamics, and the Design and Manufacturing of Composite Materials and Structures.

Bibliographic information

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From the reviews:

“This interesting and comprehensive book covers much more than the title might suggest. … The author has thus taken care to lay out the material in the first parts so that the reader has all notations and concepts clearly understood before delving into flexible multibody dynamics. … key systems are presented early in the text and then studied again later on so as to illustrate the particular content of each chapter. This has great pedagogical value and will undoubtedly be appreciated by students.” (Philippe A. Müllhaupt, Mathematical Reviews, Issue 2012 f)

“This is a textbook intended for graduate students studying current issues in dynamics. … the author provides numerous examples and guided problems throughout the text. The physical appearance and editing are excellent, with high-quality figures (in color) and quite readable exposition. Purchase by advanced dynamics students, by practitioners, by researchers, and by libraries is highly recommended.” (Ronald L. Huston, Zentralblatt MATH, Vol. 1209, 2011)