Classical Mechanics with Mathematica(R) - Antonio Romano

Classical Mechanics with Mathematica(R) (eBook)

Antonio Romano (Autor)

eBook Download: PDF

2012 | 1. Auflage
XIV, 520 Seiten
Birkhauser Boston (Verlag)
978-0-8176-8352-8 (ISBN)

This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject.? Developed by the author from 35 years of teaching experience, the presentation is designed to give students an overview of the many different models used through the history of the field—from Newton to Lagrange—while also painting a clear picture of the most modern developments. Throughout, it makes heavy use of the powerful tools offered by Mathematica?. The volume is organized into two parts. The first focuses on developing the mathematical framework of linear algebra and differential geometry necessary for the remainder of the book. Topics covered include tensor algebra, Euclidean and symplectic vector spaces, differential manifolds, and absolute differential calculus. The second part of the book applies these topics to kinematics, rigid body dynamics, Lagrangian and Hamiltonian dynamics, Hamilton–Jacobi theory, completely integrable systems, statistical mechanics of equilibrium, and impulsive dynamics, among others.Unique in its scope of coverage and method of approach, Classical Mechanics will be a very useful resource for graduate students and advanced undergraduates in applied mathematics and physics who hope to gain a deeper understanding of mechanics.

This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject.? Developed by the author from 35 years of teaching experience, the presentation is designed to give students an overview of the many different models used through the history of the field-from Newton to Lagrange-while also painting a clear picture of the most modern developments. Throughout, it makes heavy use of the powerful tools offered by Mathematica?. The volume is organized into two parts. The first focuses on developing the mathematical framework of linear algebra and differential geometry necessary for the remainder of the book. Topics covered include tensor algebra, Euclidean and symplectic vector spaces, differential manifolds, and absolute differential calculus. The second part of the book applies these topics to kinematics, rigid body dynamics, Lagrangian and Hamiltonian dynamics, Hamilton-Jacobi theory, completely integrable systems, statistical mechanics of equilibrium, and impulsive dynamics, among others.Unique in its scope of coverage and method of approach, Classical Mechanics will be a very useful resource for graduate students and advanced undergraduates in applied mathematics and physics who hope to gain a deeper understanding of mechanics.

Antonio Romano has been the author or coauthor of numerous books on mechanics and Mathematica, and he has taught courses in mechanics for 35 years at "Il Fredrico" University in Naples.

I Introduction to Linear Algebra and Differential Geometry.- 1 Vector Space and Linear Maps.- 2 Tensor Algebra.- 3 Skew-symmetric Tensors and Exterior Algebra.- 4 Euclidean and Symplectic Vector Spaces.- 5 Duality and Euclidean Tensors.- 6 Differentiable Manifolds.- 7 One-Parameter Groups of Diffeomorphisms.- 8 Exterior Derivative and Integration.- 9 Absolute Differential Calculus.- 10 An Overview of Dynamical Systems.- II Mechanics.- 11 Kinematics of a Point Particle.- 12 Kinematics of Rigid Bodies.- 13 Principles of Dynamics.- 14 Dynamics of a Material Point.- 15 General Principles of Rigid Body Dynamics.- 16 Dynamics of a Rigid Body.- 17 Lagrangian Dynamics.- 18 Hamiltonian Dynamics.- 19 Hamilton-Jacobi Theory.- 20 Completely Integrable Systems.- 21 Elements of Statistical Mechanics of Equilibrium.- 22 Impulsive Dynamics.- 23 Introduction to Fluid Mechanics.- A First-Order PDE.- B Fourier’s Series.- References.- Index.

Erscheint lt. Verlag	24.12.2012
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Naturwissenschaften ► Physik / Astronomie ► Mechanik
	Technik
Schlagworte	classical mechanics, Mathematica • Differential Geometry • Kinematics • Lagrangian and Hamiltonian dynamics • linear algebra • Rigid Body Dynamics
ISBN-10	0-8176-8352-6 / 0817683526
ISBN-13	978-0-8176-8352-8 / 9780817683528

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