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Analytical Dynamics

Theory and Applications

  • Book
  • © 2005

Overview

Authors:
  1. Mark D. Ardema

    1. Santa Clara University, Santa Clara, USA

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xv
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  2. Review of Newtonian Dynamics

    • Mark D. Ardema
    Pages 1-45

  3. Motion and Constraints

    • Mark D. Ardema
    Pages 47-64

  4. Virtual Displacement and Virtual Work

    • Mark D. Ardema
    Pages 65-82

  5. Variational Principles

    • Mark D. Ardema
    Pages 83-99

  6. Generalized Coordinates

    • Mark D. Ardema
    Pages 101-108

  7. Lagrange’s Equations

    • Mark D. Ardema
    Pages 109-130

  8. Formulation of Equations

    • Mark D. Ardema
    Pages 131-148

  9. Integration of Equations

    • Mark D. Ardema
    Pages 149-163

  10. Examples

    • Mark D. Ardema
    Pages 165-177

  11. Central Force Motion

    • Mark D. Ardema
    Pages 179-188

  12. Gyroscopic Motion

    • Mark D. Ardema
    Pages 189-204

  13. Stability Of Motion

    • Mark D. Ardema
    Pages 205-224

  14. Impulsive Motion

    • Mark D. Ardema
    Pages 225-243

  15. Gibbs-Appell Equations

    • Mark D. Ardema
    Pages 245-259

  16. Hamilton’s Equations

    • Mark D. Ardema
    Pages 261-280

  17. Contact Transformations

    • Mark D. Ardema
    Pages 281-295

  18. Hamilton-Jacobi Equation

    • Mark D. Ardema
    Pages 297-317

  19. Approximation Methods

    • Mark D. Ardema
    Pages 319-333

  20. Back Matter

    Pages 335-340
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Keywords

About this book

In his great work, Mecanique Analytique (1788)-^Lagrange used the term "analytical" to mean "non-geometrical." Indeed, Lagrange made the following boast: "No diagrams will be found in this work. The methods that I explain in it require neither constructions nor geometrical or mechanical arguments, but only the algebraic operations inherent to a regular and uniform process. Those who love Analysis will, with joy, see mechanics become a new branch of it and will be grateful to me for thus having extended its field." This was in marked contrast to Newton's Philosohiae Naturalis Principia Mathematica (1687) which is full of elaborate geometrical constructions. It has been remarked that the classical Greeks would have understood some of the Principia but none of the Mecanique Analytique. The term analytical dynamics has now come to mean the develop­ ments in dynamics from just after Newton to just before the advent of relativity theory and quantum mechanics, and it is this meaning of the term that is meant here. Frequent use will be made of diagrams to illus­ trate the theory and its applications, although it will be noted that as the book progresses and the material gets "more analytical", the number of figures per chapter tends to decrease, although not monotonically.

Reviews

From the reviews of the first edition:

"The book takes a classical approach to the development of the methods of analytical dynamics. … the book contains a large number of examples … and most of them are quite instructive. Many examples are worked out in full detail in the text, and an even greater number of additional examples is given in the form of problems (without solutions). … People who teach mechanics courses may find this collection of examples quite useful." (Volker Perlick, Zentralblatt MATH, Vol. 1087 (13), 2006)

Authors and Affiliations

  • Santa Clara University, Santa Clara, USA

    Mark D. Ardema

Bibliographic Information

  • Book Title: Analytical Dynamics

  • Book Subtitle: Theory and Applications

  • Authors: Mark D. Ardema

  • DOI: https://doi.org/10.1007/b116020

  • Publisher: Springer New York, NY

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer-Verlag US 2005

  • Hardcover ISBN: 978-0-306-48681-4Published: 16 November 2004

  • eBook ISBN: 978-0-306-48682-1Published: 31 October 2006

  • Edition Number: 1

  • Number of Pages: XVI, 340

  • Topics: Engineering, general, Vibration, Dynamical Systems, Control

  • Industry Sectors: Aerospace, IT & Software

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