Dynamics of the Rigid Solid With General Constraints By a Multibody - Approac

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...

Sommario

1. Elements of Mathematical Calculation
 
1.1 Vectors; Vector Operations
 
1.2 Real Rectangular Matrix
 
1.3 Square Matrix
 
1.4 Skew Matrix of Third Order
 
2. Kinematics of the Rigid Solid
 
2.1 Finite Displacements of the Points of Rigid Solid
 
2.2 Matrix of Rotation; Properties
 
2.3 Minimum Displacements; The Chasles Theorem
 
2.4 Small Displacements
 
2.5 Velocities of the Points of Rigid Solid
 
2.6 The Angular Velocity Matrix; Properties
 
2.7 Composition of the Angular Velocities
 
2.8 Accelerations of the Points of Rigid Solid
 
3. General Theorems in the Dynamics of the Rigid Solid
 
3.1 Moments of Inertia
 
3.2 Momentum; The Theorem of Momentum
 
3.3 Moment of Momentum; The Theorem of Moment of Momentum
 
3.4 The Kinetic Energy of the Rigid Solid
 
4. Matrix Differential Equations of the Motion of Rigid Solid
 
4.1 The Differential Equations Obtained from the General Theorems
 
4.2 The Lagrange Equations in the Case of the Holonomic Constraints
 
4.3 The Equivalence between the Differential Equations Obtained from the General Theorems and the Lagrange Equations
 
4.4 The Matrix Differential Equations for the Motion of the Constrained Rigid Solid
 
5. Generalized Forces; The Equilibrium of the Rigid Solid
 
5.1 The Generalized Forces in the Case of a Mechanical System
 
5.2 The General Expressions of the Generalized Forces in the case of Rigid Solid
 
5.3 Conservative Forces
 
5.4 The Equilibrium of the Constrained Rigid Solid
 
5.5 The Equilibrium of the Heavy Rigid Solid Hanged by Springs
 
6. The Motion of the Rigid Solid with Constraints at Given Proper Points
 
6.1 General Aspects; Classification
 
6.2 Mathematical Aspects; Notations
 
6.3 The Study of the Rigid Solid with a Fixed Point
 
6.4 The Rigid Solid with Two Fixed Points (the Rotational Motion of the Rigid Solid)
 
6.5 The Rigid Solid with a Given Point Situated on a Fixed Surface
 
6.6 The Rigid Solid with Several Points Situated on Fixed Surfaces (Curves)
 
6.7 The Rigid Solid with a Fixed Point and with Another Point Situated on a Fixed Surface
 
6.8 The Rigid Solid with Two Given Points Situated on a Fixed Curve
 
7. The Motion of the Rigid Solid with Constraints on Given Proper Curves
 
7.1 General Aspects; Classification
 
7.2 The Rigid Solid Supported at Fixed Points on Given Proper Curves
 
7.3 The Rigid Solid at Which Given Proper Curves Support with Sliding on Fixed Curves
 
7.4 Rolling without Sliding of a Curve on a Fixed Curve
 
7.5 The Motion of the Rigid Solid at Which the Curves Jointed to It Support with Sliding on Fixed Surfaces
 
7.6 The Rolling without Sliding of a Disk Bounded by a Spatial Curve on a Fixed Surface
 
7.7 The Rolling without Sliding of a Planar Circle Disk on a Horizontal Plan
 
7.8 The Rolling without Sliding of a Planar Elliptic Disk on a Horizontal Plan
 
7.9 The Rolling without Sliding of a Hyperboidic Curve on a Horizontal Plan
 
7.10 The Rolling without Sliding of a Planar Circle Disk on a Cylindrical Surface with Horizontal Generatrices
 
7.11 The Rolling without Sliding of Two Curves of a Rigid Solid on a Fixed Surface
 
7.12 The Rolling without Sliding of an Axle with Wheels (Disks) with Angular Deviations on a Horizontal Plan
 
7.13 The Rolling without Sliding of an Axle with Disks on a Hyperbolic Paraboloid
 
8. The Motion of the Rigid Solid with Constraints on the Bounding Surface
 
8.1 General Aspects; Classification

Dettagli sul prodotto

• Autori: N Pandrea, Nicola Pandrea, Nicolae Pandrea, Nicolae (University of Pitesti Pandrea, Nicolae Stanescu Pandrea, Pandrea Nicolae, Nicolae-Doru Stanescu, Nicolae-Doru (University of Pitesti Stanescu, Stanescu Nicolae-Doru
• Editore: Wiley, John and Sons Ltd
• Lingue: Inglese
• Formato: Copertina rigida
• Pubblicazione: 20.11.2015
• EAN: 9781118954386
• ISBN: 978-1-118-95438-6
• Pagine: 312
• Categorie: Scienze naturali, medicina, informatica, tecnica > Tecnica > Meccanica, tecnica di produzione; Mathematik, Maschinenbau, Mathematics, Mechanical Engineering, Solid Mechanics, numerische Methoden, Festkörpermechanik, Computational / Numerical Methods, Rechnergestützte / Numerische Verfahren im Maschinenbau, Numerical Methods