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Advanced Mechanics – From Euler's Determinism to Arnold's Chaos - Oxford Scholarship Online
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Advanced Mechanics: From Euler's Determinism to Arnold's Chaos

S. G. Rajeev


This book begins with the ancient parts of classical mechanics: the variational principle, Lagrangian and Hamiltonian formalisms, and Poisson brackets. The simple pendulum provides a glimpse of the beauty of elliptic curves, which will also appear later in rigid body mechanics. Geodesics in Riemannian geometry are presented as an example of a Hamiltonian system. Conversely, the path of a non-relativistic particle is a geodesic in a metric that depends on the potential. Orbits around a black hole are found. Hamilton-Jacobi theory is discussed, showing a path towards quantum mechanics and a conn ... More

Keywords: Hamiltonian formalism, Lagrangian, Poisson brackets, geodesic, three body problem, Lagrange points, symplectic integrator, chaos, Julia set, Newton's iteration

Bibliographic Information

Print publication date: 2013 Print ISBN-13: 9780199670857
Published to Oxford Scholarship Online: December 2013 DOI:10.1093/acprof:oso/9780199670857.001.0001


Affiliations are at time of print publication.

S. G. Rajeev, author
Department of Physics and Astronomy, University of Rochester