Advanced Dynamics
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Summary
Understanding the dynamic behavior of complex engineering structures, mechanisms, and components requires more than just a basic course in dynamics, and it requires more than the ability to use computer programs to obtain numerical solutions to problems encountered in practice. Advanced Dynamics extends its readers knowledge from the relatively simple concepts of basic dynamics to the more abstract ideas related to virtual displacements, virtual work, generalized coordinates, and variation principles. The authors' presentation gradually introduces the abstract concepts often intimidating to students, and, while doing so, furnish numerous exercises and worked examples that ease the difficulties often experienced when trying to apply the abstract concepts to physical systems.
While their emphasis is on students' understanding and intuition, the authors not only address the methods and means of formulating mathematical models of physical systems, they also discuss methods of solution, including a full chapter on numerical techniques. Designed for senior undergraduate and postgraduate students in mechanical engineering, Advanced Dynamics also forms a trustworthy reference for engineers and other professionals working in areas such as robotics, multibody spacecraft, altitude control, and the design of complex mechanical devices.
Table of Contents
INTRODUCTORY CONCEPTS IN DYNAMICS
Introduction
Newton's Laws of Motion
Kinematics of a Particle
Fixed Coordinate Systems
Kinematics of a Rigid Body
Kinetics of Particles
Kinetics of a Rigid Body in Plane Motion
Radius of Gyration and Center of Percussion
Dynamics of a Vibrating System
Critical Speed of a Rotating Shaft
CONCEPTS IN ANALYTICAL DYNAMICS
Degrees of Freedom
Generalized Coordinates
Constraints
Principle of Virtual Work
D'Alembert's Principle
ENERGY AND MOMENTUM
Work and Energy
Potential and Kinetic Energy
Impulse and Momentum
Wariable Mass System
Angular Impulse and Momentum
FRAMES OF REFERENCE
Transformation of Coordinates
Moving Reference Frames
Motion Relative to Terrestrial Frames
Foucault's Pendulum
ORBITAL MOTION
Motion Under Central Force
Kepler's Laws and Newton's Laws of Gravitation
Disturbed Elliptical Orbits
LAGRANGE'S EQUATIONS
Lagrange's Equations of Motion
Rayleigh Dissipation Function
Impulsive Motion
Integrals of the Motion
Application Examples
MOMENTS AND PRODUCTS OF INERTIA
Introduction
Mass Moment of Inertia
Product of Inertia
Moment of Inertia about and Arbitrary Axis
Momental Ellipsoid
Methods of Finding Principal Axes and Principal Moments of Inertia
DYNAMICS OF RIGID BODIES
Kinematics of a Rigid Body
Linear and Angular Momentum of a Rigid Body
The Kinetic Energy
Euler'sAngles
Equations of Motion for a Rigid Body
Motion of a Spinning Top
VARIATIONAL PRINCIPLES
Introduction
Stationary Values of a Function
Constrained Stationary Values
Stationary Value of a Definite Integral
Hamilton's Principle
Stationary Value of a Definite Integral of a Function Containing Higher Derivatives
Constrained Maxima and Minima of Functionals
Principle of Least Action
Hamilton's Equations
Phase Space
CANONICAL TRANSFORMATION
Introduction
Canonical Transformation
Lagrange and Poisson Brackets
Hamilton-Jacobi Theory
VIBRATION OF DYNAMICAL SYSTEMS
Introduction
Single-Degree-of-Freedom System
Multidegree-of-Freedom System
Lagrange's Method
DYNAMICS RESPONSE BY NUMERICAL METHODS
Introduction
Single-Degree-of-Freedom System
Multidegree-of-Freedom System
Explicit Schemes
Implicit Schemes]
Case Studies
INDEX
Editorial Reviews
"this reviewer thinks that this book is without doubt very useful at a time when many students, and even many scientists, think that Analytical Mechanics belongs to the past. Several interesting examples of the use of these methods may be found in this book. …can be used by senior students and also scientists involved in systems dynamics and interested in analytical methods rather than numerical methods."
- Applied Mechanical Review, July 2002
