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M. Kemal Ozgoren
Kinematics of General Spatial Mechanical Systems
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Вернуться на страницу книги Kinematics of General Spatial Mechanical Systems
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Страница 1
Table of Contents
List of Illustrations
Guide
Pages
Kinematics of General Spatial Mechanical Systems
Copyright
Страница 8
Preface
Acknowledgments
Страница 11
About the Companion Website
1 Vectors and Their Matrix Representations in Selected Reference Frames Synopsis
1.1 General Features of Notation
1.2 Vectors 1.2.1 Definition and Description of a Vector
1.2.2 Equality of Vectors
1.2.3 Opposite Vectors
1.3 Vector Products 1.3.1 Dot Product
1.3.2 Cross Product
1.4 Reference Frames
1.5 Representation of a Vector in a Selected Reference Frame
1.6 Matrix Operations Corresponding to Vector Operations 1.6.1 Dot Product
1.6.2 Cross Product and Skew Symmetric Cross Product Matrices
1.7 Mathematical Properties of the Skew Symmetric Matrices
1.8 Examples Involving Skew Symmetric Matrices 1.8.1 Example 1.1
1.8.2 Example 1.2
1.8.3 Example 1.3
2 Rotation of Vectors and Rotation Matrices Synopsis
2.1 Vector Equation of Rotation and the Rodrigues Formula
2.2 Matrix Equation of Rotation and the Rotation Matrix
2.3 Exponentially Expressed Rotation Matrix
2.4 Basic Rotation Matrices
2.5 Successive Rotations
2.6 Orthonormality of the Rotation Matrices
2.7 Mathematical Properties of the Rotation Matrices
2.7.1 Mathematical Properties of General Rotation Matrices
2.7.2 Mathematical Properties of the Basic Rotation Matrices
2.8 Examples Involving Rotation Matrices 2.8.1 Example 2.1
2.8.2 Example 2.2
2.8.3 Example 2.3
2.8.4 Example 2.4
2.9 Determination of the Angle and Axis of a Specified Rotation Matrix 2.9.1 Scalar Equations of Rotation
2.9.2 Determination of the Angle of Rotation
2.9.3 Determination of the Axis of Rotation
2.9.4 Discussion About the Optional Sign Variables
2.10 Definition and Properties of the Double Argument Arctangent Function
3 Matrix Representations of Vectors in Different Reference Frames and the Component Transformation Matrices Synopsis
3.1 Matrix Representations of a Vector in Different Reference Frames
3.2 Transformation Matrices Between Reference Frames 3.2.1 Definition and Usage of a Transformation Matrix
3.2.2 Basic Properties of a Transformation Matrix
3.3 Expression of a Transformation Matrix in Terms of Basis Vectors 3.3.1 Column‐by‐Column Expression
3.3.2 Row‐by‐Row Expression
3.3.3 Remark 3.1
3.3.4 Remark 3.2
3.3.5 Remark 3.3
3.3.6 Example 3.1
3.4 Expression of a Transformation Matrix as a Direction Cosine Matrix 3.4.1 Definitions of Direction Angles and Direction Cosines
3.4.2 Transformation Matrix Formed as a Direction Cosine Matrix
3.5 Expression of a Transformation Matrix as a Rotation Matrix 3.5.1 Correlation Between the Rotation and Transformation Matrices
3.5.2 Distinction Between the Rotation and Transformation Matrices
3.6 Relationship Between the Matrix Representations of a Rotation Operator in Different Reference Frames
3.7 Expression of a Transformation Matrix in a Case of Several Successive Rotations
3.7.1 Rotated Frame Based (RFB) Formulation
3.7.2 Initial Frame Based (IFB) Formulation
3.8 Expression of a Transformation Matrix in Terms of Euler Angles 3.8.1 General Definition of Euler Angles
3.8.2 IFB (Initial Frame Based) Euler Angle Sequences
3.8.3 RFB (Rotated Frame Based) Euler Angle Sequences
3.8.4 Remark 3.4
3.8.5 Remark 3.5
3.8.6 Remark 3.6: Preference Between IFB and RFB Sequences
3.8.7 Commonly Used Euler Angle Sequences
3.8.8 Extraction of Euler Angles from a Given Transformation Matrix
3.9 Position of a Point Expressed in Different Reference Frames and Homogeneous Transformation Matrices
3.9.1 Position of a Point Expressed in Different Reference Frames
3.9.2 Homogeneous, Nonhomogeneous, Linear, Nonlinear, and Affine Relationships
3.9.3 Affine Coordinate Transformation Between Two Reference Frames
3.9.4 Homogeneous Coordinate Transformation Between Two Reference Frames
3.9.5 Mathematical Properties of the Homogeneous Transformation Matrices
3.9.6 Example 3.2
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