Predicting Motion

ISBN-13: 9780750307161 / Angielski / Miękka / 2000 / 255 str.

D. Lambourne

Opis

Predicting Motion presents the core ideas of Newtonian mechanics, starting from Newton's laws and the idea that changes in motion are predictable given the forces that cause them. Richly illustrated with questions and answers for self-assessment, it carefully introduces concepts, such as kinetics and potential energy, linear momentum, torque (the rotational analogue of force), and angular momentum, and explains their role in predicting motion. Although no prior knowledge of this topic is required, the book focuses on the significance of differential equations in making such predictions. It also provides an up-to-date treatment of mechanics with accounts of relativistic collisions and the implications of chaos theory for the future of the solar system and for galaxies that contain black holes.

Spis treści

Introduction -- Chapter 1 Forces and Newton’s laws -- 1 Voyager's odyssey — an example of Newton’s laws -- 2 Newton’s laws and the definition offeree -- 2.1 Underlying concepts: frames of reference and observers -- 2.2 Newton’s first law: inertia and inertial frames of reference -- 2.3 Newton’s second law: force, mass and acceleration -- 2.4 Newton’s third law: action and reaction -- 2.5 Newton’s laws and vectors: resultant force, resolution and redirection -- 2.6 Newton’s laws and rigid bodies: centre of mass -- 3 Some familiar forces -- 3.1 Weight and terrestrial gravitation -- 3.2 Universal gravitation -- 3.3 Contact forces and normal reactions -- 3.4 Friction, viscosity and air resistance -- 3.5 Forces arising from tension and compression -- 3.6 Forces in action -- 4 Forces and motion -- 4.1 Rates of change: gradients and derivatives — a reminder -- 4.2 Some familiar forms of motion -- 4.3 Derivatives and Newton’s laws: equations of motion -- 4.4 Stepping through Newton’s laws -- 5 Closing items -- Chapter 2 Work , energy and power -- 1 Escaping the Earth — an application of energy -- 2 Work and kinetic energy -- 2.1 Kinetic energy — energy due to motion -- 2.2 Work and changes in kinetic energy -- 2.3 The work done by a constant aligned force -- 2.4 The work done by a constant non-aligned force -- 2.5 Work and the scalar product of vectors -- 3 Work and potential energy -- 3.1 Conservative and non-conservative forces -- 3.2 Potential energy — energy due to configuration -- 3.3 Strain potential energy -- 3.4 The work done by a varying force -- 3.5 Gravitational potential energy -- 3.6 Force as the negative gradient of potential energy -- 3.7 The conservation of mechanical energy -- 3.8 The role of energy in predicting motion -- 4 Power -- 4.1 Power — the rate of energy transfer -- 4.2 Power and vectors -- 5 Energy in oscillating systems -- 5 .1 The energy of a simple harmonic oscillator -- 5.2 The energy of a damped harmonic oscillator -- 5.3 The energy of a driven damped harmonic oscillator -- 5.4 A note on exponential functions -- 6 Closing items -- Chapter 3 Linear momentum and collisions -- 1 Discovering the atomic nucleus — an example -- 2 Linear momentum -- 2 .1 The linear momentum of a body -- 2.2 Momentum and Newton’s second law -- 2.3 Impulse and impulsive forces -- 2.4 The momentum of a system of bodies -- 2.5 Conservation of momentum -- 2.6 The role of momentum in predicting motion -- 3 Collisions and conservation laws -- 3 .1 Elastic and inelastic collisions -- 3.2 Elastic collisions in one dimension -- 3.3 Elastic collisions in two or three dimensions -- 3.4 Inelastic collisions -- 3.5 Collisions all around us -- 3.6 Relativistic collisions -- 4 Closing items -- Chapter 4 Torque and angular momentum -- 1 Precession — an example of rotational dynamics -- 2 Torque -- 2 .1 The turning effect of a force -- 2.2 Torque and levers -- 2.3 A vector definition of torque -- 2.4 Torque and angular motion -- 2.5 A note on vector and scalar products -- 3 Equilibrium and statics -- 3.1 Equilibrium conditions -- 3.2 Static equilibrium conditions -- 3.3 The stability of equilibrium -- 3.4 Static structures -- 4 Rotational energy and moments of inertia -- 4 .1 Rotational energy of particles -- 4.2 Rotational energy of rigid bodies -- 4.3 Torque, moment of inertia and angular acceleration -- 4.4 The role of rotational energy in the prediction of motion -- 4.5 Flywheels and energy storage -- 5 Angular momentum -- 5 .1 Angular momentum of particles -- 5.2 Angular momentum of rigid bodies -- 5.3 Torque and the rate of change of angular momentum -- 5.4 Conservation of angular momentum -- 5.5 Tops, gyroscopes and precession -- 6 Closing items -- Chapter 5 Chaotic motion -- 1 Is motion always predictable? -- 2 What is chaos? -- 2.1 A linear map -- 2.2 The logistic map -- 2.3 Some features of chaos -- 2.4 Fractals -- 2.5 State spaces and trajectories -- 2.6 Strange attractors -- 3 Examples of chaos -- 3.1 Dripping taps and beating hearts -- 3.2 Chaos in the Solar System -- 3.3 Chaos in galaxies -- 4 Closing items -- Chapter 6 Consolidation and skills development -- 1 Introduction -- 2 Overview of Chapters 1 to 5 -- 3 Problem-solving skills -- 4 Basic skills and knowledge test -- 5 Interactive questions -- 6 Physical problems -- Answers to questions -- Acknowledgements – Index.

O autorze

Lambourne, Robert