Meccanica (2009) 44: 623–625
DOI 10.1007/s11012-009-9194-2
BOOK REVIEW
Anders Klarbring: Models of mechanics. (Solid mechanics
and its applications, vol 138)
Springer
Thomas Pence
Received: 9 January 2009 / Published online: 27 January 2009
© Springer Science+Business Media B.V. 2009
Approximately a decade ago, the book Five Equations
That Changed the World: the Power and Poetry of
Mathematics by M. Guillen enjoyed a bit of vogue as
a rather whimsical chronicle into the lives and times
of Isaac Newton, Daniel Bernoulli, Michael Farady,
Rudolf Clausius, and Albert Einstein. Now, given the
above names, it is amusing to guess the five equations.
Your guess for Bernoulli and Einstein would almost
certainly be correct. You might think that the equa-
tion for Newton is also straightforward: F = ma or
more generally some version of momentum balance. If
that was your guess, then you would be mistaken since
Guillen selects the inverse square law of gravitational
attraction as the equation for his chronicle on New-
ton. This probably makes for a more interesting story
about Newton, but I would suspect that many read-
ers of Meccanica would have chosen Newton’s second
law over universal gravitation (in Guillen’s defense,
his book is entitled “Five Equations...” not “The Five
Equations...”). As a remedy for any lack of attention
to the issue of momentum balance I can suggest the
text, Models of Mechanics by Anders Klarbring from
the Springer series on Solid Mechanics and its Appli-
cations.
In fact, Klarbring’s book is a clear and concise in-
troduction into the foundations of classical mechan-
T. Pence ( )
Department of Mechanical Engineering, Michigan State
University, East Lansing, MI, USA
e-mail: pence@egr.msu.edu
ics for discrete particles, fluids, and solids (both de-
formable and rigid). It is aimed at the intermedi-
ate level, although it is likely that even seasoned re-
searchers will appreciate the philosophically unified
approach to the various systems that are considered.
The treatment emphasizes the distinction between uni-
versal laws and laws that are particular to the sys-
tem under consideration. The universal laws are in-
troduced early in the development as the conserva-
tion of mass, Euler’s law of linear momentum (the
force resultant gives the time rate change of linear
momentum), and Euler’s law of angular momentum
(the torque resultant about a fixed point gives the time
rate change of angular momentum with respect to the
same point). These universal laws are to be imple-
mented in the context of a general cutting principle
that is able to isolate arbitrary free bodies for all of
the systems mentioned above. Geometrical concepts
for bodies and their placements are introduced grace-
fully with notations that apply well to the different
types of bodies that require consideration: point mass
collections, one-dimensional continua, and higher di-
mensional continua. In addition to the usual kinematic
concepts encountered in rigid body mechanics and
in continuum mechanics, an early introduction to the
concept of more generalized director fields associated
with Cosserat continua is included.
The book devotes several chapters to the conse-
quences of the universal laws in these various systems
with little or no consideration of particular laws that