The area of analysis and control of mechanical systems using differential geometry is flourishing.

This book collects many results over the last decade and provides a comprehensive introduction to the area.

The area of analysis and control of mechanical systems using differential geometry is flourishing.

This book collects many results over the last decade and provides a comprehensive introduction to the area.

This monograph provides some useful tools for performing global geometric analysis on real analytic manifolds.  At the core of the methodology of the book is a variety of descriptions for the topologies for the space of real analytic sections of a real analytic vector bundle and for the space of real analytic mappings between real analytic manifolds.  Among the various descriptions for these topologies is a development of geometric seminorms for the space of real analytic sections. To illustrate the techniques in the book, a number of fundamental constructions in differential geometry are shown to induce continuous mappings on spaces of real analytic sections and mappings.Aimed at researchers at the level of Doctoral students and above, the book introduces the reader to the challenges and opportunities of real analytic analysis and geometry.