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A Brief on Tensor Analysis [electronic resource] /
There are three changes in the second edition. First, with the help of readers and colleagues-thanks to all-I have corrected typographical errors and made minor changes in substance and style. Second, I have added a fewmore Exercises,especially at the end ofChapter4.Third, I have appended a section on Differential Geometry, the essential mathematical tool in the study of two-dimensional structural shells and four-dimensional general relativity. JAMES G. SIMMONDS vii Preface to the First Edition When I was an undergraduate, working as a co-op student at North Ameri can Aviation, I tried to learn something about tensors. In the Aeronautical Engineering Department at MIT, I had just finished an introductory course in classical mechanics that so impressed me that to this day I cannot watch a plane in flight-especially in a turn-without imaging it bristling with vec tors. Near the end of the course the professor showed that, if an airplane is treated as a rigid body, there arises a mysterious collection of rather simple looking integrals called the components of the moment of inertia tensor.
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| Format: | Texto biblioteca |
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New York, NY : Springer New York : Imprint: Springer,
1994
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| Subjects: | Mathematics., Mathematical analysis., Analysis (Mathematics)., Analysis., |
| Online Access: | http://dx.doi.org/10.1007/978-1-4419-8522-4 |
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Mathematics. Mathematical analysis. Analysis (Mathematics). Mathematics. Analysis. Mathematics. Mathematical analysis. Analysis (Mathematics). Mathematics. Analysis. |
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Mathematics. Mathematical analysis. Analysis (Mathematics). Mathematics. Analysis. Mathematics. Mathematical analysis. Analysis (Mathematics). Mathematics. Analysis. Simmonds, James G. author. SpringerLink (Online service) A Brief on Tensor Analysis [electronic resource] / |
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There are three changes in the second edition. First, with the help of readers and colleagues-thanks to all-I have corrected typographical errors and made minor changes in substance and style. Second, I have added a fewmore Exercises,especially at the end ofChapter4.Third, I have appended a section on Differential Geometry, the essential mathematical tool in the study of two-dimensional structural shells and four-dimensional general relativity. JAMES G. SIMMONDS vii Preface to the First Edition When I was an undergraduate, working as a co-op student at North Ameri can Aviation, I tried to learn something about tensors. In the Aeronautical Engineering Department at MIT, I had just finished an introductory course in classical mechanics that so impressed me that to this day I cannot watch a plane in flight-especially in a turn-without imaging it bristling with vec tors. Near the end of the course the professor showed that, if an airplane is treated as a rigid body, there arises a mysterious collection of rather simple looking integrals called the components of the moment of inertia tensor. |
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Texto |
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Mathematics. Mathematical analysis. Analysis (Mathematics). Mathematics. Analysis. |
| author |
Simmonds, James G. author. SpringerLink (Online service) |
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Simmonds, James G. author. SpringerLink (Online service) |
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Simmonds, James G. author. |
| title |
A Brief on Tensor Analysis [electronic resource] / |
| title_short |
A Brief on Tensor Analysis [electronic resource] / |
| title_full |
A Brief on Tensor Analysis [electronic resource] / |
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A Brief on Tensor Analysis [electronic resource] / |
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A Brief on Tensor Analysis [electronic resource] / |
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brief on tensor analysis [electronic resource] / |
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New York, NY : Springer New York : Imprint: Springer, |
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1994 |
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http://dx.doi.org/10.1007/978-1-4419-8522-4 |
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AT simmondsjamesgauthor abriefontensoranalysiselectronicresource AT springerlinkonlineservice abriefontensoranalysiselectronicresource AT simmondsjamesgauthor briefontensoranalysiselectronicresource AT springerlinkonlineservice briefontensoranalysiselectronicresource |
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KOHA-OAI-TEST:1948742018-07-30T23:20:15ZA Brief on Tensor Analysis [electronic resource] / Simmonds, James G. author. SpringerLink (Online service) textNew York, NY : Springer New York : Imprint: Springer,1994.engThere are three changes in the second edition. First, with the help of readers and colleagues-thanks to all-I have corrected typographical errors and made minor changes in substance and style. Second, I have added a fewmore Exercises,especially at the end ofChapter4.Third, I have appended a section on Differential Geometry, the essential mathematical tool in the study of two-dimensional structural shells and four-dimensional general relativity. JAMES G. SIMMONDS vii Preface to the First Edition When I was an undergraduate, working as a co-op student at North Ameri can Aviation, I tried to learn something about tensors. In the Aeronautical Engineering Department at MIT, I had just finished an introductory course in classical mechanics that so impressed me that to this day I cannot watch a plane in flight-especially in a turn-without imaging it bristling with vec tors. Near the end of the course the professor showed that, if an airplane is treated as a rigid body, there arises a mysterious collection of rather simple looking integrals called the components of the moment of inertia tensor.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 -- Alternative 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 Alternative Formula for Computing the Christoffel Symbols -- A Change of Coordinates -- Transformation of the Christoffel Symbols -- Exercises -- IV The Gradient, the Del Operator, Covariant Differentiation, and the Divergence Theorem -- The Gradient -- Linear and Nonlinear Eigenvalue Problems -- The Del 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 -- Differential Geometry -- Exercises.There are three changes in the second edition. First, with the help of readers and colleagues-thanks to all-I have corrected typographical errors and made minor changes in substance and style. Second, I have added a fewmore Exercises,especially at the end ofChapter4.Third, I have appended a section on Differential Geometry, the essential mathematical tool in the study of two-dimensional structural shells and four-dimensional general relativity. JAMES G. SIMMONDS vii Preface to the First Edition When I was an undergraduate, working as a co-op student at North Ameri can Aviation, I tried to learn something about tensors. In the Aeronautical Engineering Department at MIT, I had just finished an introductory course in classical mechanics that so impressed me that to this day I cannot watch a plane in flight-especially in a turn-without imaging it bristling with vec tors. Near the end of the course the professor showed that, if an airplane is treated as a rigid body, there arises a mysterious collection of rather simple looking integrals called the components of the moment of inertia tensor.Mathematics.Mathematical analysis.Analysis (Mathematics).Mathematics.Analysis.Springer eBookshttp://dx.doi.org/10.1007/978-1-4419-8522-4URN:ISBN:9781441985224 |