This course develops a modeling approach to capture collisional interactions in mechanical systems and applies this to the analysis, simulation, and control of multibody mechanical systems. The discussion emphasizes low-speed impacts, for which any damage is highly localized, and spans from the rigid-body limit for stiff and compact structures to the elastic response of flexible structures. The methods and ideas developed here find wide use in the design, analysis, and control of man-made and biological mechanisms ranging from microelectromechanical systems to the study of crashworthiness of vehicles. In the idealized mathematical limit, mechanical systems with impacts exhibit a range of behaviors not found in "smooth" systems, for example, the occurrence of infinitely many collisions in finite time, infinitely unstable periodic trajectories, and structurally stable chaotic dynamics. The theoretical and numerical analysis of the system dynamics necessitates a mathematical toolbox that is sensitive to the dramatic effects of recurrent impacts. The course includes a discussion of methods of analysis of piecewise-smooth dynamical systems and recently documented control strategies that seek to take advantage of recurrent impacts for achieving a desired system response in example nano- and microelectromechanical devices.
TEXTBOOKS: Stronge, Impact Mechanics, Cambridge University Press (required) Brogliato
Impacts in Mechanical Systems, Springer (required)
Borgliato, Nonsmooth Mechanics: Dynamics & Control, Springer (recommended)
Di Bernardo, Budd, Champneys & Kowalczyk, Piecewise-smooth Dynamical Systems: Theory & Applications, (recommended)