A Course of Mathematics for Engineers and Scientists

Chapter I. The Foundations of Mechanics Introduction Fundamental Concepts Newton's Laws of MotionChapter 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 SystemsChapter 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 StrutsChapter 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 CurvesChapter 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 OrbitChapter 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 SystemChapter 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 MotionsChapter 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 FreedomChapter 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 - RocketsAnswers to the ExercisesIndex