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STATICS AND DYNAMICS—7TH EDITION 11 KINEMATICS OF PARTICLES 11.1 Introduction to Dynamics 11.2 11.3 11.4 11.5 11.6 11.7 11.8 Rectilinear Motion of Particles Position, Velocity, and Acceleration Determination of the Motion of a Particle Uniform Rectilinear Motion Uniformly Accelerated Rectilinear Motion Motion of Several Particles Graphical Solution of Rectilinear-Motion Problems Other Graphical Methods 11.9 11.10 11.11 11.12 11.13 11.14 Curvilinear Motion of Particles Position Vector, Velocity, and Acceleration Derivatives of Vector Functions Rectangular Components of Velocity and Acceleration Motion Relative to a Frame in Translation Tangential and Normal Components Radial and Transverse Components Review and Summary Review Problems Computer Problems 12 KINETICS OF PARTICLES: NEWTON’S SECOND LAW 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10 Introduction Newton’s Second Law of Motion Linear Momentum of a Particle. Rate of Change of Linear Momentum Systems of Units Equations of Motion Dynamic Equilibrium Angular Momentum of a Particle. Rate of Change of Angular Momentum Equations of Motion in Terms of Radial and Transverse Components Motion under a Central Force. Conservation of Angular Momentum. Newton’s Law of Gravitation 12.11 Trajectory of a Particle under a Central Force 12.12 Application to Space Mechanics 12.13 Kepler’s Laws of Planetary Motion Review and Summary Review Problems Computer Problems 13 KINETICS OF PARTICLES: ENERGY AND MOMENTUM METHODS 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 13.10 13.11 13.12 13.13 13.14 13.15 Introduction Work of Force Kinetic Energy of a Particle. Principle of Work and Energy. Applications of the Principle of Work and Energy Power and Efficiency Potential Energy Conservative Forces Conservation of Energy Motion under a Conservative Central Force. Application to Space Mechanics Principle of Impulse and Momentum Impulsive Motion Impact Direct Central Impact Oblique Central Impact Problems Involving Energy and Momentum Review and Summary Review Problems Computer Problems 14 SYSTEMS OF PARTICLES 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 Introduction Application of Newton’s Laws to the Motion of a System of Particles. Effective forces. Linear and Angular Momentum of a System of Particles Motion of the Mass Center of a System of Particles Angular Momentum of a System of Particles about Its Mass Center Conservation of Momentum for a System of Particles Kinetic Energy of a System of Particles Work-Energy Principle. Conservation of Energy for a System of Particles. Principles of Impulse and Momentum for a System of Particles 14.10 Variable Systems of Particles 14.11 Steady Stream of Particles 14.12 Systems Gaining or Losing Mass Review and Summary Review Problems Computer Problems 15 KINEMATICS OF RIGID BODIES 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 15.10 15.11 15.12 15.13 15.14 Introduction Translation Rotation about a Fixed Angle Equations Defining the Rotation of a Rigid Body about a Fixed Axis General Plane Motion Absolute and Relative Velocity in Plane Motion Instantaneous Center of Rotation in Plane Motion Absolute and Relative Acceleration in Plane Motion Analysis of Plane Motion in Terms of a Parameter Rate of Change of a Vector with Respect to a Rotating Frame Plane Motion of a Particle Relative to a Rotating Frame. Coriolis Acceleration. Motion about a Fixed Point General Motion Three-Dimensional Motion of a Particle Relative to a Rotating Frame. Coriolis Acceleration. 15.15 Frame of Reference in General Motion Review and Summary Review Problems Computer Problems 16 PLANE MOTION OF RIGID BODIES: FORCES AND ACCELERATIONS 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 Introduction Equations of Motion for a Rigid Body Angular Momentum of a Rigid Body Plane Motion of a Rigid Body. D’Alembert’s Principle A Remark on the Axioms of the Mechanics of Rigid Bodies Solution of Problems Involving the Motion of a Rigid Body Systems of Rigid Bodies Constrained Plane Motion Review and Summary Review Problems Computer Problems 17 Plane Motion of Rigid Bodies: Energy and Momentum Methods 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8 17.9 17.10 17.11 17.12 Introduction Principle of Work and Energy for a Rigid Body Work of Forces Acting on a Rigid Body Kinetic Energy of a Rigid Body in Plane Motion Systems of Rigid Bodies Conservation of Energy Power Principle of Impulse and Momentum for the Plane Motion of a Rigid Body Systems of Rigid Bodies Conservation of Angular Momentum Impulsive Motion Eccentric Impact Review and Summary Review Problems Computer Problems 18 Kinetics of Rigid Bodies in Three Dimensions 18.1 18.2 18.3 Introduction Angular Momentum of a Rigid Body in Three Dimensions Application of the Principle of Impulse and Momentum to the Three-Dimensional Motion of a Rigid Body 18.4 Kinetic Energy of a Rigid Body in Three Dimensions 18.5 Motion of a Rigid Body in Three Dimensions 18.6 Euler’s Equations of Motion. Extension of d’Alembert’s Principle to the Motion of a Rigid Body in Three Dimensions 18.7 Motion of a Rigid Body about a Fixed Point 18.8 Rotation of a Rigid Body about a Fixed Axis 18.9 Motion of a Gyroscope. Eulerian Angles 18.10 Steady Precession of a Gyroscope 18.11 Motion of an Axisymmetical Body under No Force Review and Summary Review Problems Computer Problems 19 MECHANICAL VIBRATIONS 19.1 Introduction Vibrations without Damping Free Vibrations of Particles. Simple Harmonic Motion Simple Pendulum (Approximate Solution) Simple Pendulum (Exact Solution) Free Vibrations of Rigid Bodies Application of the Principle of Conservation of Energy Forced Vibrations Damped Vibrations 19.8 Damped Free Vibrations 19.9 Damped Forced Vibrations 19.10 Electrical Analogues 19.2 19.3 19.4 19.5 19.6 19.7 Review and Summary Review Problems Computer Problems Appendix A: Some Useful Definitions and Properties of Vector Algebra Appendix B: Moments of Inertia of Masses Appendix C: Fundamentals of Engineering Appendix Index Answers to Problems