Mechanics is the study of the motion of physical objects. As such, the subject finds its applications in all areas of physics and engineering. This book provides a complete guide to mechanics, necessary for any applied mathematics student. The author has written a detailed account of classical analytical mechanics that will appeal to the modern student aided by his years of experience as a lecturer in the subject. Topics covered include Newton's, Lagrange's and Hamilton's equations of motion, kinematics, oscillation, particle mechanics and rigid body motion in two and three dimensions. A thorough understanding of the theory is provided by supporting the classical laws of motion with plenty of relevant examples and case studies. Matlab code is also used to illustrate key ideas and solutions to exercises are available to lecturers and course instructors. Solutions to exercices are available from the Web.
Table of Contents
Part I. Newtonian Mechanics of a Single Particle: 1. The algebra and calculus of vectors; 2. Velocity, acceleration and scalar angular velocity; 3. Newton's laws of motion and the law of gravitation; 4. Problems in particle dynamics; 5. Linear oscillations; 6. Energy conservation; 7. Orbits in a central field; 8. Non-linear oscillations and phase space; Part II. Multi-particle Systems: 9. The energy principle; 10. The linear momentum principle; 11. The angular momentum principle; Part III. Analytical mechanics: 12. Lagrange's equations and conservation principle; 13. The calculus of variations and Hamilton's principle; 14. Hamilton's equations and phase space; Part IV. Further Topics: 15. The general theory of small oscillations; 16. Vector angular velocity and rigid body kinematics; 17. Rotating reference frames; 18. Tensor algebra and the inertia tensor; 19. Problems in rigid body dynamics; Appendix: centres of mass and moments of inertia; Answers to the problems; Bibliography; Index.
Douglas Gregory is Professor of Mathematics at the University of Manchester. He is a researcher of international standing in the field of elasticity, and has held visiting positions at New York University, the University of British Columbia, and the University of Washington. He is highly regarded as a teacher of applied mathematics: this, his first book, is the product of many years ' teaching experience.