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Informationen zum Autor Nicolae Pandrea , Mechanical engineer, PhD. eng., Professor at the University of Piteºti. Member of the Academy of Technical Sciences in Romania, has published 250 papers in Romania, U.S.A. and Europe and 7 books. Member of the Romanian Society of Acoustics. Winner of the "Traian Vuia" prize of the Romanian Academy. Co-author of the book Numerical Analysis with Applications in Mechanics and Engineering (Wiley, 2013). Nicolae-Doru Stãnescu , Mechanical engineer, Mathematician, PhD. eng., PhD. math., Professor at the University of Piteºti, has published 200 papers in Romania, Europe and U.S.A. and 11 books. Member of the International Institute of Acoustics and Vibrations, U.S.A, Member of the Société des Ingénieurs des l'Automobile, France. Winner of the "Traian Vuia" prize of the Romanian Academy. Co-author of the book Numerical Analysis with Applications in Mechanics and Engineering (Wiley, 2013). Klappentext Covers both holonomic and non-holonomic constraints in a study of the mechanics of the constrained rigid body.* Covers all types of general constraints applicable to the solid rigid* Performs calculations in matrix form* Provides algorithms for the numerical calculations for each type of constraint* Includes solved numerical examples* Accompanied by a website hosting programs Zusammenfassung Covers both holonomic and non-holonomic constraints in a study of the mechanics of the constrained rigid body. Inhaltsverzeichnis Preface xi 1 Elements of Mathematical Calculation 1 1.1 Vectors: Vector Operations 1 1.2 Real Rectangular Matrix 4 1.3 Square Matrix 6 1.4 Skew Matrix of Third Order 10 Further Reading 12 2 Kinematics of the Rigid Solid 15 2.1 Finite Displacements of the Points of Rigid Solid 15 2.2 Matrix of Rotation: Properties 16 2.2.1 General Properties 16 2.2.2 Successive Displacements 17 2.2.3 Eigenvalues: Eigenvectors 18 2.2.4 The Expression of the Matrix of Rotation with the Aid of the Unitary Eigenvector and the Angle of Rotation 20 2.2.5 Symmetries: Decomposition of the Rotation into Two Symmetries 24 2.2.6 Rotations About the Axes of Coordinates 25 2.3 Minimum Displacements: The Chasles Theorem 27 2.4 Small Displacements 33 2.5 Velocities of the Points of Rigid Solid 34 2.6 The Angular Velocity Matrix: Properties 37 2.6.1 The Matrices of Rotation About the Axes of Coordinates 37 2.6.2 The Angular Velocity Matrix: The Angular Velocity Vector 38 2.6.3 The Matrix of the Partial Derivatives of the Angular Velocity 39 2.7 Composition of the Angular Velocities 41 2.8 Accelerations of the Points of Rigid Solid 42 Further Reading 43 3 General Theorems in the Dynamics of the Rigid Solid 45 3.1 Moments of Inertia 45 3.1.1 Definitions: Relations Between the Moments of Inertia 45 3.1.2 Moments of Inertia for Homogeneous Rigid Solid Bodies 47 3.1.3 Centers of Weight 47 3.1.4 Variation of the Moments of Inertia Relative to Parallel Axes 49 3.1.5 Variation of the Moments of Inertia Relative to Concurrent Axes 50 3.1.6 Principal Axes of Inertia: Principal Moments of Inertia 52 3.2 Momentum: The Theorem of Momentum 54 3.3 Moment of Momentum: The Theorem of Moment of Momentum 56 3.4 The Kinetic Energy of the Rigid Solid 57 Further Reading 58 4 Matrix Differential Equations of the Motion of Rigid Solid 61 4.1 The Differential Equations Obtained from the General Theorems 61 4.1.1 General Aspects 61 4.1.2 The Differential Equations 62 4.2 The Lagrange Equations in the Case of the Holonomic Constraints 63 4.3 The Equivalence between the Differential Equations Obtained from the General Theorems and th...
