Analytical
Dynamics
of
Discrete Systems
Reinhardt
M.
Rosenberg
University
of
California. Berkeley
Volume 4
in
Mathematical Concepts
and
Methods
in
Science
and
Engineering
Analytical Dynamics
of
Discrete Systems. providing
seniors and beginning graduate students in engineering
and the natural sciences with an advanced textbook
in dynamics, examines the development
of
classical
particle mechanics from Newton to Lagrange. Every
concept
is
clearly defmed before it
is
used, every
sig-
nificant result
is
stated mathematically
as
well
as
verbally, and the domain
of
applicability
of
each
is
explicitly stated. Most
of
the chapters contain a large
number
of
carefully worked out examples,
as
well
as
a set
of
suggested exercises.
The author adopts a geometrical approach to the study
of
dynamics.
He
provides an orderly transition from
Newtonian to Lagrangean mechanics by demonstrat-
ing
the need for a baSically different classification
of
forces in these two theories and the necessity
of
replacing Newton's third law by d'Alembert's prin-
ciple. In the first
seven
chapters,
he
includes detailed
reviews
of
• Newtonian mechanics, with attention paid to
the historical setting in which it developed
• the representation
of
motion
as
a trajectory in
configuration space, event space, and other
spaces
• constraints
• rigid body kinematics and kinetics
The major portion
of
the book deals with the theory
and application
of
Lagrangean mechanics, beginning
with precise defmitions
of
"virtual displacements,"
"virtual velocity," and "virtual work." The author
then discusses the principles
of
Hamilton and
of
least
action, the theory
of
contemporaneous and non-
contemporaneous variations, the theory
of
generalized
coordinates and forces, and derivations
of
Lagrange's
equations. Special chapters on celestial problems,
gyrodynamics, and impulsive motion are included
as
well.
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