This text focuses on conservation laws in magnetohydrodynamics, gasdynamics and hydrodynamics. A grasp of new conservation laws is essential in fusion and space plasmas, as well as in geophysical fluid dynamics; they can be used to test numerical codes, or to reveal new aspects of the underlying physics, e.g., by identifying the time history of the fluid elements as an important key to understanding fluid vorticity or in investigating the stability of steady flows. The ten Galilean Lie point symmetries of the fundamental action discussed in this book give rise to the conservation of energy, momentum, angular momentum and center of mass conservation laws via Noether´s first theorem. The advected invariants are related to fluid relabeling symmetries - so-called diffeomorphisms associated with the Lagrangian map - and are obtained by applying the Euler-Poincare approach to Noether´s second theorem. The book discusses several variants of helicity including kinetic helicity, cross helicity, magnetic helicity, Ertels´ theorem and potential vorticity, the Hollman invariant, and the Godbillon Vey invariant. The book develops the non-canonical Hamiltonian approach to MHD using the non-canonical Poisson bracket, while also refining the multisymplectic approach to ideal MHD and obtaining novel nonlocal conservation laws. It also briefly discusses Anco and Bluman´s direct method for deriving conservation laws. A range of examples is used to illustrate topological invariants in MHD and fluid dynamics, including the Hopf invariant, the Calugareanu invariant, the Taylor magnetic helicity reconnection hypothesis for magnetic fields in highly conducting plasmas, and the magnetic helicity of Alfvén simple waves, MHD topological solitons, and the Parker Archimedean spiral magnetic field. The Lagrangian map is used to obtain a class of solutions for incompressible MHD. The Aharonov-Bohm interpretation of magnetic helicity and cross helicity is discussed. In closing, examples of magnetosonic N-waves are used to illustrate the role of the wave number and group velocity concepts for MHD waves. This self-contained and pedagogical guide to the fundamentals will benefit postgraduate-level newcomers and seasoned researchers alike.
Excerpt from Theoretische Mechanik, Vol. 1: Kinematik und Statik Die Verlagshandlung hat der Ausstattung des vorliegenden Buches die gewohnte Sorgfalt angedeihen lassen und, wenn es nicht ohne Erfolg bleiben sollte, so gebührt ihr ein großer Teil des Verdienstes. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
John Taylor has brought to his new book, Classical Mechanics , all of the clarity and insight that made his Introduction to Error Analysis a best-selling text. Classical Mechanics is intended for students who have studied some mechanics in an introductory physics course and covers such topics as conservation laws, oscillations, Lagrangian mechanics, two-body problems, non-inertial frames, rigid bodies, normal modes, chaos theory, Hamiltonian mechanics, and continuum mechanics. A particular highlight is the chapter on chaos, which focuses on a few simple systems, to give a truly comprehensible introduction to the concepts that we hear so much about. At the end of each chapter is a large selection of interesting problems for the student, classified by topic and approximate difficulty, and ranging from simple exercises to challenging computer projects. Taylor´s Classical Mechanics is a thorough and very readable introduction to a subject that is four hundred years old but as exciting today as ever. He manages to convey that excitement as well as deep understanding and insight.
Dieses ausgereifte Lehrbuch bringt in prägnant kurzer und mathematisch verständlicher Darstellung die strömungstechnischen Grundlagen. In der aktuellen Auflage wurde ein Abschnitt zu Dissipation und Viskosen Potentialströmungen ergänzt. Aufgaben mit Lösungen helfen den Lernstoff richtig anzuwenden und fördern das Verständnis.