Foundations of Classical Mechanics - Deshmukh, P. C. (2019)
"Freshman students who have just finished high school need a short and rapid, but also thorough and comprehensive, exposure to major advances not only since Copernicus, Kepler, Galileo, and Newton, but also, since Maxwell, Einstein and Schrodinger. Through a judicious selection of topics, this book endeavors to induct freshman students into this excitement. This text does not merely teach the laws of physics, it attempts to show how they were unravelled. Thus, it brings out how empirical data led to Kepler's laws, to Galileo's law of inertia, how Newton's insights led to the principle of causality and determinism. It illustrates how symmetry considerations lead to conservation laws, and further how the laws of nature can be extracted from these connections. The intimacy between mathematics and physics is revealed throughout the book, with an emphasis on beauty, elegance and rigor. The role of mathematics in the study of nature is further highlighted in the discussions on fractals and Madelbrot sets. In its formal structure the text discusses essential topics of classical mechanics such as laws of Newtonian mechanics, conservation laws, symmetry principles, Euler-Lagrange equation, wave motion, superposition principle, and Fourier analysis. It extensively covers concepts of fluid mechanics, electrodynamics, special theory of relativity, general theory of relativity and Lorentz transformations. A chapter on chaos explains the concept of exploring laws of nature using Fibonacci sequence, Lyapunov exponent and fractal dimensions. More than 100 solved problems and 250 unsolved exercises are interspersed throughout the book for better understanding of concepts"--
Laws of mechanics and symmetry principles -- Mathematics--the very language of physics! -- Real effects of pseudo-forces--description of motion in accelerated frame of reference -- Small oscillations and wave motion -- Damped and driven oscillations; resonances -- The variational principle -- Angular momentum and rigid body dynamics -- The gravitational interaction in Newtonian mechanics -- Complex behaviour of simple system -- Gradient operator, methods of fluid mechanics and electrodynamics -- Rudiments of fluid mechanics -- Basic principles of electrodynamics -- Introduction to the special theory of relativity -- A glimpse of the general theory of relativity.
Keywords: Mechanics; Physics