Lagrangian And Hamiltonian Mechanics

Melvin G Calkin (Dalhousie Univ, Canada)

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English

World Scientific Publishing Co Pte Ltd
07 January 1996

Mathematics & Sciences; Classical mechanics; Mechanical engineering

This book takes the student from the Newtonian mechanics typically taught in the first and the second year to the areas of recent research. The discussions of topics such as invariance, Hamiltonian-Jacobi theory, and action-angle variables is especially complete; the last includes a discussion of the Hannay angle, not found in other texts. The final chapter is an introduction to the dynamics of nonlinear nondissipative systems. Connections with other areas of physics which the student is likely to be studying at the same time, such as electromagnetism and quantum mechanics, are made where possible. There is thus a discussion of electromagnetic field momentum and mechanical hidden momentum in the quasi-static interaction of an electric charge and a magnet. This discussion, among other things explains the ""(e/c)A"" term in the canonical momentum of a charged particle in an electromagnetic field. There is also a brief introduction to path integrals and their connection with Hamilton's principle, and the relation between the Hamilton-Jacobi equation of mechanics, the eikonal equation of optics, and the Schrodinger equation of quantum mechanics.

By: Melvin G Calkin (Dalhousie Univ Canada)
Imprint: World Scientific Publishing Co Pte Ltd
Country of Publication: Singapore
Dimensions: Height: 230mm, Width: 155mm, Spine: 20mm
Weight: 476g
ISBN: 9789810226725
ISBN 10: 9810226721
Pages: 228
Publication Date: 07 January 1996
Audience: College/higher education , A / AS level
Format: Hardback
Publisher's Status: Active

Newton's laws; the principle of virtual work and D'Alembert's principle; Lagrange's equations; the principle of stationary action or Hamilton's principle; invariance transformations and constants of the motion; Hamilton's equations; canonical transformations; Hamilton-Jacobi theory; action-angle variables; non-integrable systems.