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Classical mechanics = from particles to continua and regularity to chaos /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Classical mechanics/ by Govind S. Krishnaswami.
其他題名:	from particles to continua and regularity to chaos /
作者:	Krishnaswami, Govind S.
出版者:	Singapore :Springer Nature Singapore : : 2025.,
面頁冊數:	xxv, 792 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Mechanics. -
電子資源:	https://doi.org/10.1007/978-981-97-4476-3
ISBN:	9789819744763

Classical mechanics = from particles to continua and regularity to chaos /
Krishnaswami, Govind S.

Classical mechanicsfrom particles to continua and regularity to chaos /[electronic resource] :by Govind S. Krishnaswami. - Singapore :Springer Nature Singapore :2025. - xxv, 792 p. :ill., digital ;24 cm. - Texts and readings in physical sciences,v. 222366-8857 ;. - Texts and readings in physical sciences ;volume 22..

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.

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.

ISBN: 9789819744763

Standard No.: 10.1007/978-981-97-4476-3doiSubjects--Topical Terms:

525881
Mechanics.

LC Class. No.: QC125.2

Dewey Class. No.: 531

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520 $a 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.
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