Classical Mechanics & Special Relativity

Educational level: Bachelor

Classical mechanics is the starting point of physics. Over the centuries, via Newton’s three fundamental laws formulated around 1687, we have built a solid framework describing the material world around us. This textbook includes animations, demos and exercises for studying introductory classical mechanics. Moreover, we will consider the first steps of Einstein’s Special Theory of Relativity published 1905.

This book starts from the three laws of Newton and builds up classical mechanics from scratch. Its content carefully constructs the classical mechanics from Newtons laws, providing a rigorous, fundamental framework.  Emphasis is placed on working with the basic concepts of momentum, energy and angular momentum. Special attention is paid to oscillations, collisions including non-ideal ones and the Kepler problem. Rigid body dynamics is extensively discussed. The use of polar coordinates is extensively discussed.

Non-inertial frames of reference are treated starting from linearly accelerating ones and moving to the rotating frames of reference. The centrifugal and Coriolis forces are introduced and explained.

In the second part, the switch to special relativity is made. The problems coming out of Maxwells equations for electro-magnetic waves are used as the step towards modern mechanics. The Lorentz Transformation, where events in 4-dimensional space, time dilation and length contraction are discussed. Furthermore, the book introduces the world of four-vectors, deriving the four-velocity and four-momentum. Velocity transformation, Doppler shift and relativistic collision form the final parts of the book.