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Tensor calculus and analytical dynamics

Author: J G Papastavridis
Publisher: Boca Raton, Fla. : CRC Press, ©1999.
Series: Library of engineering mathematics.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
Of Conventions, Notations, and Basic Formulae -- Ch. 1. Introduction and Background -- Ch. 2. Tensor Algebra -- Ch. 3. Tensor Analysis -- Ch. 4. Introduction to Analytical Dynamics -- Ch. 5. Particle on a Curve and on a Surface -- Ch. 6. Lagrangean Mechanics: Kinematics -- Ch. 7. Lagrangean Mechanics: Kinetics.
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Document Type: Book
All Authors / Contributors: J G Papastavridis
ISBN: 0849385148 9780849385148
OCLC Number: 39313632
Description: xlvii, 386 pages : illustrations ; 24 cm.
Contents: Tensors and Geometry --
Tensors and Physics --
Tensors and Mechanics --
Exterior Forms (Cartan Calculus) --
Some Algebra --
Symmetry and Antisymmetry --
The Kronecker Delta --
The Levi-Civita Permutation Symbols --
The Generalized Kronecker Delta --
The Generalized Permutation Symbols --
Linear Equations, Cramer's Rule --
Functional Determinants (Jacobians) --
Derivatives of Determinants --
Some Geometry --
Primitive Concepts --
Set --
Group (G) --
Space --
Algebraic Definition --
Coordinate System(s) (CS) --
Manifold --
Coordinate Transformation(s) (CT) --
Systems of Coordinates vs. Frames of Reference --
Successive CT, Group Property --
Admissible CT --
Invariance --
Entity, or Object, Invariance --
Form Invariance --
Manifold Orientation --
Tensor Calculus (TC) --
Subspaces in a Manifold; Curves, Surfaces, etc. --
Special Cases --
Tensor Algebra --
Introduction: Affine and Euclidean, or Metric, Vector Spaces --
Vectors --
0. Sum --
0'. Product with a Scalar --
0". Scalar, or Dot, Product --
Affine and Euclidean Point Spaces --
Linear Independence, Dimension and Basis --
Local Basis, or Frame --
Vector Subspace of an X[subscript n] --
Complementary Vector Subspaces --
Vector Algebra in a Euclidean Vector Space --
Dot Product --
Covariant and Contravariant Components of a Vector --
Dual of (or to) a Basis --
Change of Basis --
Introduction to Coordinate Transformations--Affine/Rectilinear Coordinates --
General Curvilinear (Nonlinear) Coordinate Transformations (CT) --
Curvilinear Coordinates and Their Differentials.
Series Title: Library of engineering mathematics.
Responsibility: John G. Papastavridis.
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Abstract:

Introduces classical tensor calculus and its principal applications in the Lagrangean dynamics of discrete systems under positional or velocity constraints. This book focuses on formal structure and  Read more...

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"This is a deep and complete workin view of the fact that very few books in tensor analysis have appeared recently, the present monograph is one of the most up to datehighly recommended" -L.Y. Bahar Read more...

 
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