This is an intuitively motivated presentation of many topics in
classical mechanics and related areas of control theory and
calculus of variations. All topics throughout the book are treated
with zero tolerance for unrevealing definitions and for proofs
which leave the reader in the dark. Some areas of particular
interest are: an extremely short derivation of the ellipticity of
planetary orbits; a statement and an explanation of the “tennis
racket paradox''; a heuristic explanation (and a rigorous
treatment) of the gyroscopic effect; a revealing equivalence
between the dynamics of a particle and statics of a spring; a short
geometrical explanation of Pontryagin's Maximum Principle, and
more. In the last couple of chapters, aimed at more advanced
readers, the Hamiltonian and the momentum are compared to forces in
a certain static problem. This gives a palpable physical meaning to
some seemingly abstract concepts and theorems. With minimal
prerequisites consisting of basic calculus and basic undergraduate
physics, this book is suitable for courses from an undergraduate to
a beginning graduate level, and for a mixed audience of
mathematics, physics and engineering students. Much of the
enjoyment of the subject lies in solving almost 200 problems in
this book. This book is published in cooperation with Mathematics
Advanced Study Semesters.
General
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