e-book

Classical Mechanics

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The second edition introduced one additional chapter on Perturbation Theory,
and changed the ordering of the chapter on Small Oscillations. In addition it added
a significant amount of new material which increased the number of pages by
about 68%. This third edition adds still one more new chapter on Nonlinear Dynamics
or Chaos, but counterbalances this by reducing the amount of material in
several of the other chapters. by shortening the space allocated to appendices, by
considerably reducing the bibliography, and by omitting the long lists of symbols.
Thus the third edition is comparable in size to the second.

In the chapter on relativity we have abandoned the complex Minkowski spare
in favor of the now standard real metric. Two of the authors prefer the complex
metric because of its pedagogical advantages (HG) and because it fits in well with
Clifford Algebra formulations of Physics (CPP), but the desire to prepare students
who can easily move forward into other areas of theory such as field theory and
general relativity dominated over personal preferences. Some modem notation
such as I-forms, mapping and the wedge product is introduced in this chapter.

The chapter on Chaos is a necessary addition because of the current interest
in nonlinear dynamics which has begun to play a significant role in applications
of classical dynamics. The majority of classical mechanics problems and apphcations
in the real world Include nonlineantles, and It is important for the student
to have a grasp of the complexities involved, and of the new properties that can
emerge. It is also important to realize the role of fractal dimensionality in chaos.

New sections have been added and others combined or eliminated here and
there throughout the book, with the omissions to a great extent motivated by the
desire not to extend the overall length beyond that of the second edition. Asection
was added on the Euler and Lagrange exact solutions to the three body problem.
In several places phase space plots and Lissajous figures were appended to illustrate
solutions. The damped driven pendulum was discussed as an example that
explains the workings of Josephson junctions. The symplectic approach was clarified
by writing out some of the matrices. The harmonic oscillator was treated
with anisotropy, and also in polar coordinates. The last chapter on continua and
fields was fonnulated in the modern notation introduced in the relativity chapter.
The significances of the special unitary group in two dimensions SU(2) and
the special orthogonal group in three dimensions SO(3) WE're presentf'.rl in more
up-ta-date notation, and an appendix was added on groups and algebras. Special
tables were introduced to clarify properties of ellipses, vectors, vector fields and
I-forms, canonical transformations, and the relationships between the spacetime
and symplectic approaches.

Several of the new features and approaches in this third edition had been mentioned
as possihilities in the preface to the second edition. such as properties of
group theory, tensors in non-Euclidean spaces, and "new mathematics" oftheoretical
physics such as manifolds. The reference to "One area omitted that deserves
special attention-nonlinear oscillation and associated stability questions" now
constitutes the subject matter of our new Chapter 11 "Classical Chaos." We debated
whether to place this new chapter after Perturbation theory where it fits
more logically. or before Perturbation theory where it is more likely to be covered
in class, and we chose the latter. The referees who reviewed our manuscript were
evenly divided on this question.

The mathemnatical level of the present edition is about the same as that of the
first two editions. Some of the mathematical physics, such as the discussions
of hermitean and unitary matrices, was omitted because it pertains much more
to quantum mechanics than it does to classical mechanics, and little used notations
like dyadics were curtailed. Space devoted to power law potentials, CayleyKlein
parameters, Routh's procedure, time independent perturbation theory, and
the stress-energy tensor was reduced.. In some cases reference was made to the
second edition for more details. The problems at the end of the chapters were
divided into "derivations" and "exercises:' and some new ones were added.

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Ketersediaan

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Informasi Detail

Judul Seri

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No. Panggil

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Penerbit

California : Addison Wesley., 2000

Deskripsi Fisik

x, 638 Hlm.

Bahasa

English

ISBN/ISSN

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Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

3rd ed.

Subjek

TEKNIK MESIN

Info Detail Spesifik

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Pernyataan Tanggungjawab

agus

Versi lain/terkait

Lampiran Berkas

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