Essential Dynamics and Relativity

Essential Dynamics & Relativity provides students with an introduction to the core aspects of dynamics and special relativity. The author reiterates important ideas and terms throughout and covers concepts that are often missing from other textbooks at this level. He also places each topic within the wider constructs of the theory, without jumping from topic to topic to illustrate a point. The first section of the book focuses on dynamics, discussing the basic aspects of single particle motion and analyzing the motion of multi-particle systems. The book also explains the dynamical behavior of both composite bodies (rigid bodies) and objects in non-inertial frames of reference (rotating reference frames). The second section concentrates on relativity. The author describes the ideas leading to the inception of special relativity. He also formulates fundamental aspects, such as time dilation, length contraction, Lorentz transformations, and the visual aids of Minkowski diagrams, necessary to develop more sophisticated ideas. He then develops the concepts within the context of relativistic mechanics. With many examples throughout and exercises at the end of each chapter, this text makes the often daunting and confusing ideas of dynamics and special relativity accessible to undergraduate students studying the subjects for the first time.

DYNAMICS The Galileo–Newton Formulation of Dynamics Galilean relativity Newton’s dynamical laws Gravitational and inertial mass Particle Dynamics in One Dimension Motion of a particle under a force Potential energy diagrams Tension Friction Resistive motion Escape velocity Oscillations Hooke’s law Simple harmonic motion Period of small oscillations Damped simple harmonic motion Damped simple harmonic motion with a forcing term The LCR circuit Particle Dynamics in Two and Three Dimensions Projectiles Energy and force Charged particles in an electromagnetic field Central Forces and Orbits Central forces and angular momentum Circular motion Orbital motion The inverse square law The orbital equation Perturbed orbits Kepler’s laws of planetary motion The perihelion precession of Mercury Rutherford scattering Multi-Particle SystemsConservation of linear momentum Conservation of angular momentum The centre of mass frame The two-body problem Collisions Inelastic collisions Variable mass problems Rigid Bodies Rotation of a rigid body about a fixed axis Planar motion of a rigid body Rotating Reference Frames Rates of change in a rotating frameNewton’s second law in a rotating frame The centrifugal forceThe Coriolis force RELATIVITYSpecial RelativityInception Einstein’s postulates of special relativity Lorentz transformations Minkowski diagrams (space-time diagrams) Relativistic kinematics Space-Time The light cone Proper time The four-component vector formalism Relativistic Mechanics 4-momentum Relativistic energy Massless particles Aberration Particle collisions Appendix: Conic Sections Solutions Index Exercises appear at the end of each chapter.

Peter J. O’Donnell is a Lecturer in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge, where he is also a Fellow of St. Edmund’s College. Dr. O’Donnell’s current research focuses on Lanczos potential theory, black holes, and quantum gravity.