Analytical mechanics Books
Oxford University Press Dimensional Analysis Across the Landscape of
Book SynopsisDimensional Analysis Across the Landscape of Physics introduces readers to the powerful idea that almost all physical quantities in science and engineering can be described using only five base dimensions: mass, length, time, charge, and temperature, and combinations thereof. Starting with the basics of how this foundational intellectual concept arises, it illustrates the use of dimensional analysis in approaching the solutions to textbook-level problems in physics and adjacent fields, ranging from introductory courses, through the advanced undergraduate curriculum, to advanced Physics electives. It covers the core curricular topics of classical mechanics, electricity and magnetism, thermal physics, and quantum mechanics. It includes examples of the use of dimensional analysis applied to topics from other related fields such as geosciences, meteorology, engineering, and biophysics to emphasize the utility of such methods across the proverbial landscape of physics. There is also coverage of more specialized topics, such as advanced quantum mechanics, particle physics, field theory, condensed matter physics, and astrophysics and gravitation. Many worked examples are included, as well as an extensive array of end-of-chapter problems, with a solution manual available to instructors. In addition to covering the standard topics in the undergraduate curriculum, the book explores how dimensional analysis has been used (and continues to be used) in research across all fields of physics, citing examples from the historical literature and from very recent research results. The work includes extensive references to the original papers for further study, as well as useful ancillary material, including a dimensional analysis ''dictionary'', brief introductions to data-fitting, and connections to metrology. There is an emphasis throughout on the use of modern symbolic programming to streamline the process of the solving systems of linear equations needed for a dimensional analysis approach, with several Mathematica templates provided for reader use.
£42.75
Oxford University Press Lectures on Analytical Mechanics
Book SynopsisWritten by professional physicists with over 140 years'' of teaching experience combined, this book is aimed at students and lecturers in physics. The authors present analytical mechanics as the basis for the study of theoretical physics, its methods and ideas forming the foundation of all other branches including quantum mechanics, statistical physics, and field theory.The book begins by discussing the motion of particles in a central field and scattering of particles based on Newton''s equations. It then introduces and explores Lagrange equations for various systems, linear and non-linear oscillations, Hamiltonian formalism, and the motion of a rigid body. Each topic is accompanied by problems that are suitable for seminars and testing.The book also includes five supplemental sections, which provide practical illustrations of the theoretical material. These sections can be used by teachers as the basis for conducting a specialized course, or by curious students who wish to explore di
£76.95
Oxford University Press Lectures on Analytical Mechanics
Book SynopsisWritten by professional physicists with over 140 years'' of teaching experience combined, this book is aimed at students and lecturers in physics. The authors present analytical mechanics as the basis for the study of theoretical physics, its methods and ideas forming the foundation of all other branches including quantum mechanics, statistical physics, and field theory.The book begins by discussing the motion of particles in a central field and scattering of particles based on Newton''s equations. It then introduces and explores Lagrange equations for various systems, linear and non-linear oscillations, Hamiltonian formalism, and the motion of a rigid body. Each topic is accompanied by problems that are suitable for seminars and testing.The book also includes five supplemental sections, which provide practical illustrations of the theoretical material. These sections can be used by teachers as the basis for conducting a specialized course, or by curious students who wish to explore di
£33.24
MIT Press Bicycling Science
Book Synopsis
£28.80
John Wiley & Sons Inc Statistical Mechanics
Book SynopsisUnlike most other texts on the subject, this clear, concise introduction to the theory of microscopic bodies treats the modern theory of critical phenomena. Provides up-to-date coverage of recent major advances, including a self-contained description of thermodynamics and the classical kinetic theory of gases, interesting applications such as superfluids and the quantum Hall effect, several current research applications, The last three chapters are devoted to the Landau-Wilson approach to critical phenomena. Many new problems and illustrations have been added to this edition.Table of ContentsThe Laws of Thermodynamics. Some Applications of Thermodynamics. The Problem of Kinetic Theory. The Equilibrium State of a Dilute Gas. Transport Phenomena. Classical Statistical Mechanics. Canonical Ensemble and Grand Canonical Ensemble. Quantum Statistical Mechanics. General Properties of the Partition Function. Approximate Methods. Fermi Systems. Bose Systems. Superfluids. Ising Model. Onsager Solution. Critical Phenomena. The Landau Approach. Renormalization Group. Appendix. Index.
£200.66
John Wiley & Sons Inc Analytical Routes to Chaos in Nonlinear
Book SynopsisNonlinear problems are of interest to engineers, physicists and mathematicians and many other scientists because most systems are inherently nonlinear in nature. As nonlinear equations are difficult to solve, nonlinear systems are commonly approximated by linear equations.Table of ContentsPreface ix 1 Introduction 1 1.1 Analytical Methods 1 1.1.1 Lagrange Standard Form 1 1.1.2 Perturbation Methods 2 1.1.3 Method of Averaging 5 1.1.4 Generalized Harmonic Balance 8 1.2 Book Layout 24 2 Bifurcation Trees in Duffing Oscillators 25 2.1 Analytical Solutions 25 2.2 Period-1 Motions to Chaos 32 2.2.1 Period-1 Motions 33 2.2.2 Period-1 to Period-4 Motions 35 2.2.3 Numerical Simulations 52 2.3 Period-3 Motions to Chaos 57 2.3.1 Independent, Symmetric Period-3 Motions 57 2.3.2 Asymmetric Period-3 Motions 64 2.3.3 Period-3 to Period-6 Motions 71 2.3.4 Numerical Illustrations 82 3 Self-Excited Nonlinear Oscillators 87 3.1 van del Pol Oscillators 87 3.1.1 Analytical Solutions 87 3.1.2 Frequency-Amplitude Characteristics 97 3.1.3 Numerical Illustrations 110 3.2 van del Pol-Duffing Oscillators 114 3.2.1 Finite Fourier Series Solutions 114 3.2.2 Analytical Predictions 130 3.2.3 Numerical Illustrations 143 4 Parametric Nonlinear Oscillators 151 4.1 Parametric, Quadratic Nonlinear Oscillators 151 4.1.1 Analytical Solutions 151 4.1.2 Analytical Routes to Chaos 156 4.1.3 Numerical Simulations 169 4.2 Parametric Duffing Oscillators 186 4.2.1 Formulations 186 4.2.2 Parametric Hardening Duffing Oscillators 194 5 Nonlinear Jeffcott Rotor Systems 209 5.1 Analytical Periodic Motions 209 5.2 Frequency-Amplitude Characteristics 225 5.2.1 Period-1 Motions 226 5.2.2 Analytical Bifurcation Trees 231 5.2.3 Independent Period-5 Motion 239 5.3 Numerical Simulations 246 References 261 Index 265
£98.06
Akademica Publishing Engineering Approach to Finite Element Analysis
Book Synopsis
£66.30
World Scientific Publishing Co Pte Ltd Material Geometry: Groupoids In Continuum
Book SynopsisThis monograph is the first in which the theory of groupoids and algebroids is applied to the study of the properties of uniformity and homogeneity of continuous media. It is a further step in the application of differential geometry to the mechanics of continua, initiated years ago with the introduction of the theory of G-structures, in which the group G denotes the group of material symmetries, to study smoothly uniform materials.The new approach presented in this book goes much further by being much more general. It is not a generalization per se, but rather a natural way of considering the algebraic-geometric structure induced by the so-called material isomorphisms. This approach has allowed us to encompass non-uniform materials and discover new properties of uniformity and homogeneity that certain material bodies can possess, thus opening a new area in the discipline.
£76.00
