Classical Mechanics

From Particles to Continua and Regularity to Chaos

Govind S. Krishnaswami (Autor)

Buch | Hardcover

792 Seiten

2025 | 2024 ed.
Springer Verlag, Singapore
9789819744756 (ISBN)

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This well-rounded and self-contained treatment of classical mechanics strikes a balance between examples, concepts, phenomena and formalism. While addressed to graduate students and their teachers, the minimal prerequisites and ground covered should make it useful also to undergraduates and researchers. Starting with conceptual context, physical principles guide the development. Chapters are modular and the presentation is precise yet accessible, with numerous remarks, footnotes and problems enriching the learning experience. Essentials such as Galilean and Newtonian mechanics, the Kepler problem, Lagrangian and Hamiltonian mechanics, oscillations, rigid bodies and motion in noninertial frames lead up to discussions of canonical transformations, angle-action variables, Hamilton-Jacobi and linear stability theory. Bifurcations, nonlinear and chaotic dynamics as well as the wave, heat and fluid equations receive substantial coverage. Techniques from linear algebra, differential equations, manifolds, vector and tensor calculus, groups, Lie and Poisson algebras and symplectic and Riemannian geometry are gently introduced. A dynamical systems viewpoint pervades the presentation. A salient feature is that classical mechanics is viewed as part of the wider fabric of physics with connections to quantum, thermal, electromagnetic, optical and relativistic physics highlighted. Thus, this book will also be useful in allied areas and serve as a stepping stone for embarking on research.

Govind Krishnaswami is a Professor of Physics at the Chennai Mathematical Institute, India, and is a recipient of the Apker Award and Marie Curie, EPSRC and Ramanujan Fellowships. His research in areas such as particle physics, nonlinear dynamics and fluid mechanics has often exploited ideas and tools from classical mechanics. He has taught a wide variety of subjects and is known for the clarity of his lectures and pedagogical articles in Resonance, a journal of science education.

Mechanical systems with one degree of freedom.- Kepler’s gravitational two-body problem.- Newtonian to Lagrangian and Hamiltonian mechanics.- Introduction to special relativistic mechanics.- Dynamics viewed as a vector ﬁeld on state space.- Small oscillations for one degree of freedom.- Nonlinear oscillations: pendulum and anharmonic oscillator.- Rigid body mechanics.- Motion in noninertial frames of reference.- Canonical transformations.- Angle-action variables.- Hamilton-Jacobi equation.- Normal modes of oscillation and linear stability.- Bifurcations: qualitative changes in dynamics.- From regular to chaotic motion.- Dynamics of continuous deformable media.- Vibrations of a stretched string and the wave equation.- Heat diffusion equation and Brownian motion.- Introduction to ﬂuid mechanics.

Erscheinungsdatum	05.08.2025
Reihe/Serie	Texts and Readings in Physical Sciences
Zusatzinfo	10 Illustrations, color; 157 Illustrations, black and white
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Mechanik
Schlagworte	angle-action variables • Bifurcations • Brownian motion • Canonical Transformations • classical mechanics • ﬂuid dynamics • hamiltonian • Hamilton-Jacobi equation • heat equation • Kepler problem • Lagrangian • noninertial frames • Nonlinear Dynamics • Normal Modes • Poisson Brackets • Rigid Bodies • Special relativity • Variational Principles • wave equation
ISBN-13	9789819744756 / 9789819744756
Zustand	Neuware