Movement equations 2. Mathematical and methodological supplements / Michel Borel, Georges Venizelos.

Format:

Book

Author/Creator:

Borel, Michel, author.

Vénizélos, Georges, author.

Series:

Mechanical engineering and solid mechanics series.

Mechanical Engineering And Solid Mechanics Series

Non-deformable Solid Mechanics Set ; Volume 2

Language:

English

Subjects (All):

Mathematics.

Equations.

Physical Description:

1 online resource (159 pages) : illustrations.

Edition:

1st ed.

Place of Publication:

London, England ; Hoboken, New Jersey : ISTE : Wiley, 2017.

Summary:

The formalism processing of unbuckled solids mechanics involves several mathematical tools which are to be mastered at the same time. This volume collects the main points which take place in the course of the formalism, so that the user immediately finds what he needs without looking for it. Furthermore, the book contains a methodological formulary to guide the user in his approach.

Contents:

Intro

Table of Contents

Title

Copyright

Introduction

Table of Notations

1 Vector Calculus

1.1. Vector space

1.2. Affine space of dimension 3 - free vector

1.3. Scalar product a·b

1.4. Vector product a∧b

1.5. Mixed product (a,b,c)

1.6. Vector calculus in the affine space of dimension 3

1.7. Applications of vector calculus

1.8. Vectors and basis changes

2 Torsors and Torsor Calculus

2.1. Vector sets

2.2. Introduction to torsors

2.3. Algebra torsors

2.4. Characterization and classification of torsors

2.5. Derivation torsors

3 Derivation of Vector Functions

3.1. Derivative vector: definition and properties

3.2. Derivative of a function in a basis

3.3. Deriving a vector function of a variable

3.4. Deriving a vector function of two variables

3.5. Deriving a vector function of n variables

3.6. Explicit intervention of the variable p

3.7. Relative rotation rate of a basis relative to another

4 Vector Functions of One Variable Skew Curves

4.1. Vector function of one variable

4.2. Tangent at a point M

4.3. Unit tangent vector τ(q)

4.4. Main normal vector ν(q)

4.5. Unit binormal vector β(q)

4.6. Frenet's basis

4.7. Curvilinear abscissa

4.8. Curvature, curvature center and curvature radius

4.9. Torsion and torsion radius

4.10. Orientation in (λ) of the Frenet basis

5 Vector Functions of Two Variables Surfaces

5.1. Representation of a vector function of two variables

5.2. General properties of surfaces

6 Vector Function of Three Variables: Volumes

6.1. Vector functions of three variables

6.2. Volume element

6.3. Rotation rate of the local basis

7 Linear Operators

7.1. Definition

7.2. Intrinsic properties

7.3. Algebra of linear operators

7.4. Bilinear form

7.5. Quadratic form.

7.6. Linear operator and basis change

7.7. Examples of linear operators

7.8. Vector rotation Ru,α

8 Homogeneity and Dimension

8.1. Notion of homogeneity

8.2. Dimension

8.3. Standard mechanical dimensions

8.4. Using dimensional equations

Bibliography

Index

End User License Agreement.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9781119379065

1119379067

9781119379096

1119379091

9781119379089

1119379083

OCLC:

967938483