Lagrangian and Hamiltonian Dynamics

Abstract This book explores the fascinating subject of classical mechanics, which is the pinnacle of nineteenth-century physics, from a fresh and exciting viewpoint. With its foundations laid down in ancient Greece, classical physics was truly born in the 1700s with Sir Isaac Newton’s discoveries and quickly developed into the modern scientific method that is commonplace today. After the Newtonian revolution, others reformulated classical mechanics into different descriptions and new formalisms, each uncovering novel aspects of the mathematical and geometrical laws of nature. Over the last 400 years, classical physics has been used to engineer bridges, railways, engines, antennas, planes and much, much more. Classical mechanics is still a vibrant field of active research in theoretical physics and, to this day, captures the excitement of many physicists. Classical mechanics persists today due to its incredible practicality and as the physical embodiment of many fields of abstract mathematics. In this book, the reader journeys from Newton’s three laws of motion to analytical mechanics and Lagrangian and Hamiltonian dynamics, as well as the formulations of Jacobi and many other hard-working natural philosophers who lend their names to classical mechanics.