Differential geometry and kinematics of continua (Q2925242)

This book gives a concise presentation of a differential geometric analysis of holonomic and anholonomic deformations of continua. The main ingredients are: a detailed explanation of mathematical operations and examples, a derivation of results in general coordinates and then the passage to special coordinates when needed, an overview of the related literature.NEWLINENEWLINEThe first chapter outlines the motivation, objectives and contents of the book, while giving the notation and historical remarks. The second chapter is devoted to fundamental definitions and derivations of differential geometry useful for applications to continuum mechanics and physics. The third chapter provides a mathematical framework describing kinematics of continuous bodies undergoing holonomic deformations, whereas the fourth chapter considers geometry of anholonomic deformations. The final chapter studies kinematics of anholonomic deformationsNEWLINENEWLINEFormer results in holonomic deformations are presented in a systematic and easy-to-follow way. For anholonomic deformations new result are combined with the old ones in a fashion that a unified notation is used and relations to the literature are pointed out when useful.