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.

Inhalt

Basics of Continuum Mechanics (A. K. Belyaev).- A Treatise on the Equations of Balance and on the Jump Relations in Continuum Mechanics (H. Irschik).- The Rayleigh-Ritz Technique and the Lagrange Equationsin Continuum Mechanics: Formulations for Material and Non-Material Volumes (H. Irschik, H. J. Holl, F. Hammelmüller).- Basics of Analytical Mechanics (A. K. Belyaev).- Compensation of Deformations in Elastic Solids and Structures in the Presence of Rigid-Body Motions (H. Irschik,U. Pichler, M. Nader, Ch. Zehetner).- Computational Dynamics of an Elasto-Plastic Structural Element With Rigid-Body Degrees-of-Freedom (J. Gerstmayr, H. Irschik, M. Dibold).- High Frequency Dynamics of Engineering Structures (A. K. Belyaev).- Basic Differential Geometry for Mechanics and Control (K. Schlacher, K. Zehetleitner).- Port-Hamiltonian Systems: Network Modeling and Control of Nonlinear Physical Systems (A. J. van der Schaft).- Periodic Motion Induced by the Painlevé Paradox (R. I. Leine, B. Brogliato, H. Nijmeijer).- Coordination of Rigid and Flexible Joint Robot Manipulators (A. Rodriguez-Angeles, H. Nijmeijer, H. A. van Essen).- Structural Control for Dynamic Hazard Mitigation (F. Casciati).- Some Applications of Differential Geometry in Control (K. Schlacher, S.Fuchshumer, J. Holl).- Some Applications of Differential Geometry in Mechanics (K. Schlacher, G.Grabmair, H. Ennsbrunner, R. Stadlmayr)