Advanced Dynamics and Control of Structures and Machines

1. Front Matter

   Pages ii-vii

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2. Basics of Continuum Mechanics

   • Alexander K. Belyaev

   Pages 1-8

3. A Treatise on the Equations of Balance and on the Jump Relations in Continuum Mechanics

   • Hans Irschik

   Pages 9-20

4. The Rayleigh-Ritz Technique and the Lagrange Equations in Continuum Mechanics: Formulations for Material and Non-Material Volumes

   • Hans Irschik, Helmut J. Holl, Franz Hammelmüller

   Pages 21-35

5. Basics of Analytical Mechanics

   • Alexander K. Belyaev

   Pages 37-52

6. Compensation of Deformations in Elastic Solids and Structures in the Presence of Rigid-Body Motions

   • Hans Irschik, Uwe Pichler, Manfred Nader, Christian Zehetner

   Pages 53-63

7. Computational Dynamics of an Elasto-Plastic Structural Element With Rigid-Body Degrees-of-Freedom

   • Johannes Gerstmayr, Hans Irschik, Markus Dibold

   Pages 65-76

8. High Frequency Dynamics of Engineering Structures

   • Alexander K. Belyaev

   Pages 77-96

9. Basic Differential Geometry for Mechanics and Control

   • Kurt Schlacher, Kurt Zehetleitner

   Pages 97-125

10. Port-Hamiltonian Systems: Network Modeling and Control of Nonlinear Physical Systems

    • A. J. van der Schaft

    Pages 127-167

11. Periodic Motion Induced by the Painlevé Paradox

    • R. I. Leine, B. Brogliato, H. Nijmeijer

    Pages 169-194

12. Coordination of Rigid and Flexible Joint Robot Manipulators

    • A. Rodriguez-Angeles, H. Nijmeijer, H. A. van Essen

    Pages 195-215

13. Structural Control for Dynamic Hazard Mitigation

    • Fabio Casciati

    Pages 217-248

14. Some Applications of Differential Geometry in Control

    • Kurt Schlacher, Stefan Fuchshumer, Johann Holl

    Pages 249-260

15. Some Applications of Differential Geometry in Mechanics

    • Kurt Schlacher, Gernot Grabmair, Helmut Ennsbrunner, Richard Stadlmayr

    Pages 261-281

This book, intended for people in engineering and fundamental sciences, presents an integrated mathematical methodology for advanced dynamics and control of structures and machines, ranging from the derivation of models up to the control synthesis problem. This point of view is particularly useful as the physical insight and the associated structural properties, related e.g. to the Lagrangian or Hamiltonian framework, can be advantageously utilized. To this end, up to date results in disciplines like continuum mechanics, analytical mechanics, thermodynamics and electrodynamics are presented exploiting the differential geometric properties, with the basic notions of this coordinate-free approach revisited in an own chapter. In order to illustrate the proposed methodologies, several industrial applications, e.g., the derivation of exact solutions for the deformation compensation by shaped actuation in elastic bodies, or the coordination of rigid and flexible joint robots, are discussed.

• Hamiltonian and Lagrangian systems
• mechanics and control
• nonlinear dynamic systems
• robotics
• structural dynamics
• continuum mechanics
• control
• deformation
• dynamics
• engine
• geometry
• Hamiltonian
• material
• Mathematica
• mechanics
• modeling
• robot
• thermodynamics
• complexity

• Johannes Kepler University of Linz, Austria

  Hans Irschik, Kurt Schlacher

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