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Intermediate Dynamics for Engineers A Unified Treatment of Newton-Euler and Lagrangian Mechanics

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ISBN-10: 0521874831

ISBN-13: 9780521874830

Edition: 2008

Authors: Oliver O'Reilly

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This book has sufficient material for two full-length semester courses in advanced engineering dynamics. As such it contains two tracks (which overlap in places). During the first course a Newton-Euler approach is used, followed by a Lagrangian approach in the second. In discussing rotations for the second course, time constraints permit a detailed discussion of only the Euler angle parameterization of a rotation tensor from Chapter 6 and a brief mention of the examples on rigid body dynamics discussed in Chapter 9. The text includes invaluable exercises at the end of each chapter that are highly structured and intended as a self-study aid. Validated solutions are provided, many of which…    
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Book details

Copyright year: 2008
Publisher: Cambridge University Press
Publication date: 8/4/2008
Binding: Hardcover
Pages: 408
Size: 7.25" wide x 10.00" long x 1.25" tall
Weight: 2.2
Language: English

Dynamics of a Single Particle
Kinematics of a Particle
Reference Frames
Kinematics of a Particle
Frequently Used Coordinate Systems
Curvilinear Coordinates
Representations of Particle Kinematics
Classification of Constraints
Closing Comments
Kinetics of a Particle
The Balance Law for a Single Particle
Work and Power
Conservative Forces
Examples of Conservative Forces
Constraint Forces
Dynamics of a Particle in a Gravitational Field
Dynamics of a Particle on a Spinning Cone
A Shocking Constraint
A Simple Model for a Roller Coaster
Closing Comments
Lagrange's Equations of Motion for a Single Particle
Lagrange's Equations of Motion
Equations of Motion for an Unconstrained Particle
Lagrange's Equations in the Presence of Constraints
A Particle Moving on a Sphere
Some Elements of Geometry and Particle Kinematics
The Geometry of Lagrange's Equations of Motion
A Particle Moving on a Helix
Dynamics of a System of Particles
The Equations of Motion for a System of Particles
A System of N Particles
Constraints and Constraint Forces
Conservative Forces and Potential Energies
Lagrange's Equations of Motion
Construction and Use of a Single Representative Particle
The Lagrangian
A Constrained System of Particles
A Canonical Form of Lagrange's Equations
Alternative Principles of Mechanics
Closing Remarks
Dynamics of Systems of Particles
Harmonic Oscillators
A Dumbbell Satellite
A Pendulum and a Cart
Two Particles Tethered by an Inextensible String
Closing Comments
Dynamics of a Single Rigid Body
Rotation Tensors
The Simplest Rotation
Proper-Orthogonal Tensors
Derivatives of a Proper-Orthogonal Tensor
Euler's Representation of a Rotation Tensor
Euler's Theorem: Rotation Tensors and Proper-Orthogonal Tensors
Relative Angular Velocity Vectors
Euler Angles
Further Representations of a Rotation Tensor
Derivatives of Scalar Functions of Rotation Tensors
Kinematics of Rigid Bodies
The Motion of a Rigid Body
The Angular Velocity and Angular Acceleration Vectors
A Corotational Basis
Three Distinct Axes of Rotation
The Center of Mass and Linear Momentum
Angular Momenta
Euler Tensors and Inertia Tensors
Angular Momentum and an Inertia Tensor
Kinetic Energy
Concluding Remarks
Constraints on and Potentials for Rigid Bodies
A Canonical Function
Integrability Criteria
Forces and Moments Acting on a Rigid Body
Constraint Forces and Constraint Moments
Potential Energies and Conservative Forces and Moments
Concluding Comments
Kinetics of a Rigid Body
Balance Laws for a Rigid Body
Work and Energy Conservation
Additional Forms of the Balance of Angular Momentum
Moment-Free Motion of a Rigid Body
The Baseball and the Football
Motion of a Rigid Body with a Fixed Point
Motions of Rolling Spheres and Sliding Spheres
Closing Comments
Lagrange's Equations of Motion for a Single Rigid Body
Configuration Manifold of an Unconstrained Rigid Body
Lagrange's Equations of Motion: A First Form
A Satellite Problem
Lagrange's Equations of Motion: A Second Form
Lagrange's Equations of Motion: Approach II
Rolling Disks and Sliding Disks
Lagrange and Poisson Tops
Closing Comments
Systems of Rigid Bodies
Introduction to Multibody Systems
Balance Laws and Lagrange's Equations of Motion
Two Pin-Jointed Rigid Bodies
A Single-Axis Rate Gyroscope
Closing Comments
Background on Tensors
Preliminaries: Bases, Alternators, and Kronecker Deltas
The Tensor Product of Two Vectors
Second-Order Tensors
A Representation Theorem for Second-Order Tensors
Functions of Second-Order Tensors
Third-Order Tensors
Special Types of Second-Order Tensors
Derivatives of Tensors