Hamilton’s Principle in Continuum Mechanics

ISBN-13: 9783030903084 / Angielski / Miękka / 2022 / 104 str.

Anthony Bedford

Opis

This revised, updated edition provides a comprehensive and rigorous description of the application of Hamilton’s principle to continuous media. To introduce terminology and initial concepts, it begins with what is called the first problem of the calculus of variations.  For both historical and pedagogical reasons, it first discusses the application of the principle to systems of particles, including conservative and non-conservative systems and systems with constraints. The foundations of mechanics of continua are introduced in the context of inner product spaces. With this basis, the application of Hamilton’s principle to the classical theories of fluid and solid mechanics are covered. Then recent developments are described, including materials with microstructure, mixtures, and continua with singular surfaces.

Spis treści

Mechanics of Systems of Particles .- Mathematical Preliminaries.- Mechanics of Continuous Media.-  Motions and Comparison Motions of a Mixture.- Singular Surfaces.- Index.

O autorze

Dr. Anthony Bedford is Professor Emeritus in the Department of Aerospace Engineering and Engineering Mechanics at The University of Texas at Austin, USA.

Blurb

This revised, updated edition provides a comprehensive and rigorous description of the application of Hamilton’s principle to continuous media. To introduce terminology and initial concepts, it begins with what is called the first problem of the calculus of variations.  For both historical and pedagogical reasons, it first discusses the application of the principle to systems of particles, including conservative and non-conservative systems and systems with constraints. The foundations of mechanics of continua are introduced in the context of inner product spaces. With this basis, the application of Hamilton’s principle to the classical theories of fluid and solid mechanics are covered. Then recent developments are described, including materials with microstructure, mixtures, and continua with singular surfaces.

• ​Presents a comprehensive, rigorous description of the application of Hamilton’s principle to continuous media;
• Includes recent applications of the principle to continua with microstructure, mixtures, and media with surfaces of discontinuity;
• Discusses foundations of continuum mechanics and variational methods therein in the context of linear vector spaces.