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Advanced Theoretical Mechanics
A Course of Mathematics for Engineers and Scientists
- 1st Edition - January 1, 1966
- Authors: Brian H. Chirgwin, Charles Plumpton
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 3 7 4 0 - 7
Advanced Theoretical Mechanics deals with advanced theoretical mechanics in three dimensions, making use of concepts and methods such as matrices, vectors, tensors, and… Read more
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Request a sales quoteAdvanced Theoretical Mechanics deals with advanced theoretical mechanics in three dimensions, making use of concepts and methods such as matrices, vectors, tensors, and transformation methods. The definition of a vector via the transformation law obeyed by its components is emphasized, and matrix methods are used to handle sets of components. Special attention is given to the definition of angular velocity and the proof that it can be represented by a vector. This book is comprised of 11 chapters and begins with an introduction to kinematics in three dimensions. Lagrange's equations and analytical dynamics are then presented, along with the simpler problems of three-dimensional dynamics, often with the help of rotating axes. Stability and small oscillations are also considered. The subsequent chapters focus on the dynamics of a particle and the motion of a system of particles; gyroscopic motion, free rotation, and steady motion; oscillations of a dynamical system with a finite number of degrees of freedom; and the vibrations of strings. The final chapter is devoted to analytical dynamics, paying particular attention to Hamilton's principle and equations of motion as well as the Hamilton-Jacobi equation. This monograph is intended for engineers and scientists as well as students of mathematics, physics, and engineering.
Preface
Chapter I. Kinematics in Three Dimensions
Introduction
The Transformation Law for Vectors
Finite Rotations
Successive Rotations: Euler's Angles
Angular Velocity
Relative Motion
Moving Frames of Reference
The Acceleration of a Particle
The General Motion of a Rigid Body
Angular Velocities about Non-Intersecting Axes
Chapter II. Sets of Forces: Equilibrium
Introduction
Equilibrium
Equivalent Sets of Forces
The Principle of Virtual Work
Other Sets of Line Vectors
Chapter III. The Dynamics of a Particle
General Principles
A Particle with One Degree of Freedom
The Use of Rotating and Accelerated Axes
The Spherical Pendulum
Motion on a Surface of Revolution
Motion Relative to the Rotating Earth
The Motion of a Charged Particle
Chapter IV. The Motion of a System of Particles
Description of the System
The Dynamical Variables
Conservation Laws
The Inertia Matrix
Principal Axes of Inertia
Dynamical Variables for Rigid Systems
The Motion of a Sphere
Chapter V. Gyroscopic Motion, Free Rotation and Steady Motion
Introduction
Rotation under No Forces of Bodies with Kinetic Symmetry
The Steady Motion of a Gyroscope or Top
The General Motion of a Top
Euler's Dynamical Equations
Free Rotation
More General Motions
Chapter VI. Lagrange's Equations
Generalized Methods
The Dynamical Variables
Generalized Forces
Classification of Constraints
Application of the Principle of Virtual Work
Conservation Laws
Ignoration of Coordinates
The Motion of a Charged Particle
Chapter VII. Stability of Motion
Introduction
Steady Motion with Two Degrees of Freedom
The Stability of Free Rotation of a Rigid Body
The Stability of a Top
The Gyro-Compass
The Stability of a Rolling Wheel
Chapter VIII. Impulsive Motion
Elementary Discussion
Generalized Methods
General Theorems
Chapter IX. The Oscillations of a Dynamical System with a Finite Number of Degrees of Freedom - Normal Modes
Introduction
Systems with Two Degrees of Freedom
Stability of Equilibrium: Free Oscillations of a System with n Degrees of Freedom
The Oscillations of a Linearly Constrained System—Rayleigh's Principle
A Reciprocal Theorem
Chapter X. The Vibrations of Strings
The Fundamental Concepts of Wave Motion
Transverse Vibrations
Normal Modes
Forced Vibrations and Damping
Reflection and Transmission at a Discontinuity
Longitudinal Vibrations
Application of Rayleigh's Principle
Miscellaneous Problems
Chapter XI. Analytical Dynamics
Introduction
Hamilton's Principle
The Principle of Least Action
Hamilton's Equations of Motion
Transformation Theory: Contact Transformations
Infinitesimal Contact Transformations
The Hamilton-Jacobi Equation
Answers to the Exercises
Index
- No. of pages: 518
- Language: English
- Edition: 1
- Published: January 1, 1966
- Imprint: Pergamon
- eBook ISBN: 9781483137407
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