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A Course of Mathematics for Engineers and Scientists
Theoretical Mechanics
- 1st Edition - January 1, 1963
- Authors: Brian H. Chirgwin, Charles Plumpton
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 3 9 8 6 - 9
A Course of Mathematics for Engineers and Scientists, Volume 3: Theoretical Mechanics introduces the concepts of virtual work, generalized coordinates and the derivation of… Read more
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Request a sales quoteA Course of Mathematics for Engineers and Scientists, Volume 3: Theoretical Mechanics introduces the concepts of virtual work, generalized coordinates and the derivation of generalized forces from the potential energy function. This book is composed of 10 chapters and begins with the principles of mechanics, plane statistics, virtual work, and continuously distributed forces. The succeeding chapters deal with the motion of a particle and the uniplanar motion of a rigid body, as well as the concept of particle dynamics. These topics are followed by discussions of the motions of interacting particles and the principles of stability. The final chapter describes the impulsive motion of a system of particles and collision between bodies. This book will be of value to mathematics and engineering students.
Chapter I. The Foundations of Mechanics
Introduction
Fundamental Concepts
Newton's Laws of Motion
Chapter II. Plane Statics and Virtual Work
The Equilibrium of a Particle and a Rigid Body
Equivalent Sets of Forces
The Work Done by a Force
The Principle of Virtual Work
Potential Energy
Statically Indeterminate Systems
Chapter III. Continuously Distributed Forces
A Uniform, Flexible, Inelastic String Hanging Under Gravity
Variable Loading - The Suspension Bridge
The Equilibrium of Heavy Elastic Strings
Strings in Contact with Surfaces
Shearing Forces and Bending Moments
The Bending of Thin Elastic Beams
Pure Flexure
The Properties of the Heaviside Unit Function and its Derivative
Macaulay's Method
Clapeyron's Theorem of Three Moments
Struts
Chapter IV. Kinematics
Introduction
Velocity and Acceleration
Special Representations
The Hodograph
Relative Motion
Angular Velocity
Instantaneous Center: Centrodes
Chapter V. Particle Dynamics I: Motion with One Degree of Freedom
Introduction; Conservative Forces
Motion on a Straight Line
Simple Harmonic Motion and Damping
Motion in a Circle
Motion on Other Curves
Chapter VI. Particle Dynamics II: Motion with Two Degrees of Freedom
Introduction
The Motion of a Projectile in a Resisting Medium
Motion Under a Central Force - General Theorems
The Differential Equations of Central Orbits
The Direct Law of Force
The Inverse Square Law
Newton's Theorem of the Revolving Orbit
Chapter VII. Systems of Particles
The Motion of Two Interacting Particles
The Encounter of Two Interacting Particles
The Motion of Connected Particles
The General Theory of Systems of Particles
The Motion of a Rigid Lamina
Applications of the Principles of Conservation of Linear Momentum, Angular Momentum and Energy to the Motion of Rigid Bodies
Moments and Products of Inertia of a Plane System
Chapter VIII. The Uniplanar Motion of a Rigid Body
Introduction
The Motion of a Rigid Body about a Fixed Axis
Systems without a Fixed Axis of Rotation
Conservative Systems of Force
Rolling and Sliding Motion
The Use of the Instantaneous Center: Initial Motions
Chapter IX. Stability
The Concept of Stability
Stability of Equilibrium
Oscillations about Stable Equilibrium
Motion on a Rotating Curve
Perturbation of an Orbit
Systems with more than One Degree of Freedom
Chapter X. Impulsive Motion and Variable Mass
Introduction
The Impulsive Motion of a System of Particles
Collisions between Particles
Collisions between Bodies: Energy Changes
The Motion of a Body with Changing Mass - Rockets
Answers to the Exercises
Index
- No. of pages: 382
- Language: English
- Edition: 1
- Published: January 1, 1963
- Imprint: Pergamon
- eBook ISBN: 9781483139869
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