Preface to the second edition
Since the publication of the ﬁrst edition six years ago several readers com-
mented on the book and recommended improvements in a future edition.
Academic readers requested expanding the mathematical foundation with a
chapter dedicated to analytic solutions. Industrial readers desired a deeper
exploration of the variational foundation of equations of motion for various
engineering disciplines. Finally some reviewers suggested expanding the com-
putational techniques section.
The modiﬁcations to the second edition reﬂect these requests. The major
additions are in two new chapters (6 and 10) and two new Sections (7.5 and
12.5). Chapter 6 discusses a variety of analytic solutions to problems of cal-
culus of variations and Chapter 10 derives various equations of motion from
variational principles. Section 7.5 describes the boundary integral method
and Section 12.5 contains a detailed description of the ﬁnite element method.
The typographical errors found in the ﬁrst edition have been corrected and
a strong eﬀort was made to avoid introducing any in the new material. The
new chapters and sections were indexed and more references were added to
make this work as complete as possible.