CLASSICAL MECHANICS FOUNDATIONS

Classical mechanics from Newton's laws to Lagrange, Hamilton and chaos, with every step shown and every problem solved.

Many mechanics books skip the algebra between the lines, leave figures unexplained and give answers without solutions. This book closes those gaps inside its own covers. Each mathematical tool is taught when it is first needed, each derivation is written out with the reason for every step, each figure is computed from the equations it illustrates and followed by a paragraph on how to read it, and each result is labelled as a definition, a law, a model or a derivation.

Classical Mechanics Foundations builds the subject in 18 chapters and seven parts:

• Motion and its laws: kinematics in several coordinate systems, Newton's laws, air resistance, variable mass and numerical solution


• Conservation laws: momentum and collisions, work and energy landscapes, angular momentum and rotation


• Oscillations: free, damped and driven oscillators, resonance and Fourier analysis


• Orbits and accelerated frames: gravitation, Kepler orbits, rotating frames, Coriolis forces and tides


• Analytical mechanics: the calculus of variations, Lagrangian and Hamiltonian mechanics, Noether's theorem, phase space


• Extended systems: rigid bodies and spinning tops, coupled oscillators, normal modes and waves


• Beyond the classical ideal: nonlinear dynamics and chaos, relativistic mechanics, and where classical mechanics meets computation, biology and the cosmos

Inside you will find:

• 116 worked examples, each set out as Strategy, Solution and Check


• 342 practice problems at three levels, with full step-by-step solutions in Appendix A


• 100 original computed figures and 215 numbered equations, with every number checked by calculation


• Bridge boxes linking mechanics to engineering, life science, medicine, Earth and space science and computation: robot arms, tuned mass dampers, the inner ear, heart rhythms, the cochlea, exoplanets, spacecraft attitude and GPS clocks


• Appendices of constants, Solar-System data, mathematical methods and notation, plus a list of symbols, glossary and index

Written for undergraduates in physics and engineering, for students in the life, Earth and computer sciences who need mechanics, and for self-learners who want to understand motion properly rather than memorise formulas.