Differential geometry and kinematics of continua - Clayton, John D. 1976- (World Scientific, 2015)
Preface; Contents; 1. Introduction; 1.1 Motivation, Objectives, and Scope; 1.2 Historical Remarks; 1.3 Notation; 1.4 Summary; 2. Geometric Fundamentals; 2.1 Configurations, Coordinates, and Metrics; 2.1.1 Motion and coordinates; 2.1.2 Metric tensors; 2.1.3 Shifter tensors; 2.2 Linear Connections; 2.2.1 Connection coefficients and covariant derivatives; 2.2.2 Torsion and curvature; 2.2.3 Identities for connection coefficients and curvature; 2.2.4 Riemannian geometry; 2.2.5 Euclidean space; 2.3 Differential Operators and Related Notation; 2.3.1 Gradient, divergence, curl, and Laplacian