A Brief on Tensor Analysis - Softcover

Simmonds, J.G.

Softcover

ISBN 10: 1468401424 ISBN 13: 9781468401424

Verlag: Springer, 2012

Inhaltsangabe

I Introduction: Vectors and Tensors.- Three-Dimensional Euclidean Space.- Directed Line Segments.- Addition of Two Vectors.- Multiplication of a Vector v by a Scalar ?.- Things That Vectors May Represent.- Cartesian Coordinates.- The Dot Product.- Cartesian Base Vectors.- The Interpretation of Vector Addition.- The Cross Product.- Alternate Interpretation of the Dot and Cross Product. Tensors.- Definitions.- The Cartesian Components of a Second Order Tensor.- The Cartesian Basis for Second Order Tensors.- Exercises.- II General Bases and Tensor Notation.- General Bases.- The Jacobian of a Basis Is Nonzero.- The Summation Convention.- Computing the Dot Product in a General Basis.- Reciprocal Base Vectors.- The Roof (Contravariant) and Cellar (Covariant) Components of a Vector.- Simplification of the Component Form of the Dot Product in a General Basis.- Computing the Cross Product in a General Basis.- A Second Order Tensor Has Four Sets of Components in General.- Change of Basis.- Exercises.- III Newton's Law and Tensor Calculus.- Rigid Bodies.- New Conservation Laws.- Nomenclature.- Newton's Law in Cartesian Components.- Newton's Law in Plane Polar Coordinates.- The Physical Components of a Vector.- The Christoffel Symbols.- General Three-Dimensional Coordinates.- Newton's Law in General Coordinates.- Computation of the Christoffel Symbols.- An Alternate Formula for Computing the Christoffel Symbols.- A Change of Coordinates.- Transformation of the Christoffel Symbols.- Exercises.- IV The Gradient Operator, Covariant Differentiation, and the Divergence Theorem.- The Gradient.- Linear and Nonlinear Eigenvalue Problems.- The Del or Gradient Operator.- The Divergence, Curl, and Gradient of a Vector Field.- The Invariance of ? · v, ? × v, and ?v.- The Covariant Derivative.- The Component Forms of ? · v, ? × v, and ?v.- The Kinematics of Continuum Mechanics.- The Divergence Theorem.- Exercises.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2012
• ISBN 10: 1468401424
• ISBN 13: 9781468401424
• Einband: Paperback
• Sprache: Englisch
• Kontakt zum Hersteller: Nicht verfügbar