Rigid Body Dynamics 1st Edition by Joaquim Batlle, Ana Barjau Condomines ISBN 1108902251 9781108902250

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Product details:

ISBN 10: 1108902251

ISBN 13: 9781108902250

Author:  Joaquim A. Batlle, Ana Barjau Condomines 

Rigid Body Dynamics 1st Edition: Building up from first principles and simple scenarios, this comprehensive introduction to rigid body dynamics gradually introduces readers to tools to address involved real-world problems, and cutting-edge research topics. Using a unique blend of conceptual, theoretical and practical approaches, concepts are developed and rigorously applied to practical examples in a consistent and understandable way. It includes discussion of real-world applications including robotics and vehicle dynamics, and over 40 thought-provoking fully worked examples to cement readers’ understanding. Providing a wealth of resources allowing readers to confidently self-assess – including over 100 problems with solutions, over 400 high quality multiple choice questions, and end-of-chapter puzzles dealing with everyday situations – this is an ideal companion for undergraduate students in aerospace, civil and mechanical engineering.

 

Rigid Body Dynamics 1st Edition Table of contents:

1 Particle Dynamics
1.1 Fundamental Assumptions Underlying Newtonian Dynamics

• Principle of Causality
• Principle of Absolute Simultaneity
• Other Assumptions

1.2 Galilean and Non-Galilean Reference Frames
1.3 Dynamics of a Free Particle: Newton’s First Law (Principle of Inertia)
1.4 Dynamics of Interacting Particles

• Galileo’s Principle of Relativity
• Mach’s Empirical Propositions

1.5 Closing the Formulation of Dynamics: From Mach’s Axiomatics to Newton’s Laws, and Principle of D

• Newton’s Third Law
• Newton’s Second Law
• Principle of Determinacy

1.6 Usual Galilean Reference Frames
1.7 Interaction Forces between Particles: Kinematic Dependency

• Restrictions on the Position Dependency (Fig. 1.8)
• Restrictions on the Velocity Dependency (Fig. 1.9)

1.8 Contact Forces between Particles and Extended Bodies
1.9 Formulation of Interaction Forces

• Gravitational Force
• Interaction Force through Springs
• Interaction Force through Dampers
• Interaction Force through Actuators

1.10 Characterization and Limit Conditions of Constraint Forces: Friction Forces

• Particle-Surface Interaction: Force Associated with Impenetrability
• Particle-Surface Interaction: Force Associated with Friction
• Particle-Curve Interaction
• Constraints between Particles through Intermediate Elements
• Analytical Characterization of Constraint Forces

1.11 Dynamics in Non-Galilean Reference Frames: Inertial Forces

• Relationship between Inertial Forces Associated with Non-Galilean Reference Frames with a Relative T

1.12 Examples
Appendix 1A Gravitational Field Outside and Inside the Earth’s Surface

• External Gravitational Field (Spherical Mass Distribution)
• Internal Gravitational Field (Uniform Mass Distribution)

Appendix 1B: Dynamics in the Terrestrial Reference Frame (TRF)

• First Approximation
• Second Approximation

Quiz Questions
Exercises
Puzzles
Quiz Questions: Answers
Exercises: Results
Puzzles: Solutions

2 Interaction Forces between Rigid Bodies
2.1 Torsor of a System of Forces
2.2 Formulation of Interaction Torsors: Gravitational Torsor, and Torsion Springs, Dampers, and Driv

• Gravitational Torsor
• Torsion Springs, Dampers, and Drivers

2.3 Constraint Torsor between Two Rigid Bodies: Indeterminacy and Ill-Conditioning

• Full Redundancy
• Tangent Redundancy (or Ill-Conditioning)

2.4 Constraint Torsors between Rigid Bodies: Analytical Characterization

• Linear and Geometric Constraint Torsors
• Straightforward Characterization

2.5 Constraint Auxiliary Elements
2.6 Constraints in Multibody Systems: Indeterminacy and Ill-Conditioning
2.7 Limit Conditions in Multiple-Point Unilateral Constraints: Contact Loss and Overturning

• Overturning

2.8 Additional Limit Conditions: Sliding, Rolling, and Pivoting

• Translational Sliding with Isotropic Friction
• Rolling
• Pivoting

Appendix 2A Gravitational Moments
Quiz Questions
Puzzles
Quiz Questions: Answers
Puzzles: Solutions

3 Mass Distribution
3.1 Center of Mass
3.2 Analytical Calculation of the Center of Mass: Pappus-Guldin Theorems

• Linear, Surface, and Volumetric Elements
• Symmetries
• Pappus-Guldin Theorems

3.3 Inertia Tensor

• Moments of Inertia
• Products of Inertia

3.4 Steiner’s Theorem
3.5 Rotation of Axes
3.6 Principal Directions of Inertia: Symmetrical and Spherical Rotors

• Rigid Bodies with Symmetry Planes in the Mass Distribution
• Symmetrical Rotor
• Spherical Rotor

3.7 Practical Tips to Calculate the Inertia Tensor about a Point Q

• Choice of the Vector Basis
• Choice of the Point Q
• Superposition: Negative Masses
• Symmetrical Partitions

3.8 Inertia Ellipsoid
Quiz Questions
Exercises
Quiz Questions: Answers
Exercises: Results

4 Vector Theorems
4.1 Linear Momentum Theorem in Galilean Reference Frames
4.2 Angular Momentum Theorem in Galilean Reference Frames

• AMT about a Point O Fixed to a RGal
• AMT about a Point Q Moving Relative to RGal
• AMT about the Center of Mass G

4.3 Barycentric Decomposition of the Angular Momentum
4.4 Angular Momentum of a Rigid Body
4.5 Dynamic Properties of the Principal Axes of Inertia (PAI)
4.6 Time Integral of the Vector Theorems: Force Impulse and Angular Impulse

• A Remark on the Word ”Conservation”

4.7 Vector Theorems in General Non-Galilean Reference Frames
Appendix 4A Static and Dynamic Balancing of a Rotor
Quiz Questions
Exercises
Puzzles
Quiz Questions: Answers
Exercises: Results
Puzzles: Solutions

5 Work-Energy Theorem
5.1 Work-Energy Theorem: Kinetic Energy, Work and Power done by a Force
5.2 Barycentric Decomposition of the Kinetic Energy
5.3 Work-Energy Theorem in Non-Galilean Reference Frames with Translational Motion Relative to a Gal
5.4 Kinetic Energy of a Rigid Body
5.5 Work Associated with the Internal Forces
5.6 Work Associated with the Forces on a Rigid Body
5.7 Work Associated with External Constraint and Friction Forces
5.8 Work Associated with Conservative Forces: Conservative Systems
5.9 Potential Energy

• Potential Energy Increment Associated with a Uniform Gravitational Field
• Potential Energy Increment Associated with the Earth’s Gravitational Field
• Potential Energy Increment Associated with a Linear Spring

5.10 One-DoF Systems with Constant Mechanical Energy: Equilibrium Configurations and Stability
5.11 The Utopia of Perpetual Motion

• Impossibility of the Perpetual Motion Machine of the First Kind
• Impossibility of the Perpetual Motion Machine of the Second Kind

5.12 Work-Energy Theorem in Non-Galilean Reference Frames
Appendix 5A Rotation Stability in a Free Rigid Body
Quiz Questions
Exercises
Puzzles
Quiz Questions: Answers
Exercises: Results
Puzzles: Solutions

6 The Method of Virtual Power
6.1 D’Alembert Inertial Forces: Formulation of the Method of Virtual Power
6.2 The Equations of Motion through the MVP

• Principle of Virtual Power (or Lagrange-d’Alembert Principle)

6.3 The Constraint Forces through the MVP
6.4 Torsor of D’Alembert Inertial Forces in a Rigid Body

• Particular Case: Planar Motion
  Quiz Questions
  Exercises
  Puzzles
  Quiz Questions: Answers
  Exercises: Results
  Puzzles: Solutions

7 Lagrange’s Equations
7.1 Generalized Forces in the Method of Virtual Power
7.2 Components of the Generalized D’Alembert Inertial Force
7.3 Components of the Generalized Conservative Force
7.4 Lagrange’s Equations
7.5 Constraint Forces from Lagrange’s Equations
7.6 Lagrange’s Equations with Multipliers
7.7 Hamilton’s Principle
Appendix 7A Equilibrium Configurations
Quiz Questions
Exercises
Quiz Questions: Answers
Exercises: Results

8 Introduction to Percussive Dynamics
8.1 Introduction to Percussive Problems
8.2 Percussive Behavior of Constraints
8.3 Percussions Associated with Dry Friction
8.4 Percussive Formulation of the Vector Theorems

• Linear Momentum Theorem
• Angular Momentum Theorem
• A Comment on Non-Galilean Frames in Percussive Dynamics

8.5 Percussion Center
8.6 Percussive Formulation of the Work-Energy Theorem

• Pseudowork Associated with a Percussion
• Pseudowork Associated with an Action-Reaction Percussive Pair

8.7 Energy Balance: Newton’s Restitution Rule
8.8 Percussive Formulation of the Method of Virtual Power
8.9 Percussive Formulation of Lagrange’s Equations
8.10 Multiple-Point Collisions

 

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