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ISBN 10: 1786300338
ISBN 13: 9781786300331
Author: Michel Borel, Georges Venizelos
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.
1 Vector Calculus
1.1. Vector space
1.2. Affine space of dimension 3 – free vector
1.3. Scalar product
1.4. Vector product
1.5. Mixed product
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
4.4. Main normal vector
4.5. Unit binormal vector
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
8 Homogeneity and Dimension
8.1. Notion of homogeneity
8.2. Dimension
8.3. Standard mechanical dimensions
8.4. Using dimensional equations
Bibliography
equations of motion book
movement book
the movement book pdf
the book of movement exploration pdf
movements equation
Tags: Michel Borel, Georges Venizelos, Movement, Equations
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