Classical Mechanics

ISBN-13: 9780710202802 / Angielski / Miękka / 1984 / 117 str.

B. P. Cowan; Brian Cowan

Opis

The study of mechanics plays a central role in physics for a whole variety of reasons. It was one of the earliest of the quantitative sciences, and had immediate practical applications. These ranged from the study of the motion of projectiles in warfare to the motion of the planets, predicting the seasons, eclipses, etc. At the present time, even though superseded on the very small scale by quantum theory and on the very large scale by the theory of relativity, the mechanics of Newton is perfectly adequate for treating a wide spectrum of problems from the - '"etic theory of gases to the motion of space vehicles. Furthermore, the science of mechanics is regarded by many as the epitome of a good scientific theory and for this reason is studied by philosophers and social scientists alike as an exemplar of the 'scientific method'. We shall commence in Chapter 1 with a brief historical outline of the development of mechanics, mentioning the names and dates of the main participants and summarizing their contributions. Preface vii Chapter 1 Newton's laws 1. 1 Historical introduction Primitive ideas about mechanics were exemplified by the state- ments of Aristotle (384-322 Be), who asserted that a force was necessary to maintain motion. Furthermore, he believed that there were different laws for heavenly and earthly bodies.

Spis treści

1 Newton’s laws.- 1.1 Historical introduction.- 1.2 Kinematics and the use of vectors.- 1.3 Newton’s laws of motion.- 1.4 Galilean relativity.- 1.5 The formulation of Mach.- 2 Energy and momentum.- 2.1 Conservation laws.- 2.2 Kinetic energy and work.- 2.3 Conservative forces.- 2.4 Momentum and momentum conservation.- 2.5 Angular momentum.- 3 Dynamics of a single particle.- 3.1 One-dimensional motion.- 3.2 General solution of one-dimensional motion.- 3.3 Harmonic motion — small oscillations.- 3.4 Central forces.- 3.5 Qualitative features of motion under a central force.- 3.6 The Kepler problem.- 3.7 Kepler’s laws.- 4 Many-particle systems.- 4.1 Centre of mass.- 4.2 The two-body problem.- 4.3 Energy of a many-particle system.- 4.4 Angular momentum.- 4.5 Friction and dissipation.- 4.6 Scattering.- 4.7 Rutherford scattering.- 4.8 Rockets and variable-mass systems.- 5 Rigid bodies and non-inertial frames.- 5.1 Rigid bodies.- 5.2 Rotating vectors.- 5.3 The inertia tensor.- 5.4 The Euler equations for rigid-body motion.- 5.5 The symmetrical top.- 5.6 Stability of rotational motion.- 5.7 Particle in a rotating frame.- 6 Lagrangian and Hamiltonian mechanics.- 6.1 Principle of least action.- 6.2 Calculus of variations.- 6.3 Recovery of Newton’s laws.- 6.4 Symmetry and conservation laws.- 6.5 Hamilton’s equations.- 6.6 Charged particle in an electromagnetic field.- 6.7 Poisson brackets.- 6.8 Connections with quantum mechanics.- Appendix 1 Exercises.- Appendix 2 Answers to exercises.