Vol.2, No 8, 1998 pp. 781
PRE-PRINCIPLES OF MECHANICS
by V. A. VUJIČIĆ
Publisher: Zavod za udžbenike i nastavna sredstva,
Matematički institut SANU, Beograd, 1998
Ranislav M. Bulatović
This book represents the synthesis of the author's views on the logical
cunception of the mechanics and the results of his research in the theory
of mechanical motion over a period of several decades. The content is so
divided that it corresponds to suggested logical structure made of: pre-principles,
basic definitions, laws of dynamics, principles, theorems; analysis of
solutions of differential equations, and stability of motion.
Pre-principles (statements evident by themselves) of existence, determinism
and invariance indicate the origin of mechanics, its basic concepts, a
priori prediction of the possibility to describe the motion, and independence
of the natural characteristics of motion of the formal method of description.
Basic definitions include only four concepts (velocity, acceleration,
impulse and inertial force), while the laws of dynamics involve only those
formulations that determine certain forces.
The main part of the book is devoted to principles of mechanics. The
principle of equilibrium is first presented (usually referred to as d'Alembert's
principle), then, after necessary additional definitions are introduced,
three variational principles are formulated, principle of work, action
and constraint. The relations representing these principles are explained
through the application to certain mechanical systems, particularly the
rheonomic systems. The rheonomic coordinate is introduced, which implies
abandoning the concepts of "freezing" the non-stationary, constraints,
and extending the configurational and phase spaces. As a result, the systems
of differential equations of motion are extended and number of furmulas
of analytical dynamics are modified. The theorem of change of impulse is
given, as well as the theorem of change of kinetic energy, theorem of guided
motion, and theorem of optimal control of motion. The concept of insufficiently
developed covariant integration is briefely presented, while the covariant
differential equations of perturbation and the author's general criterion
of stability are derived in the closing part of the book.
Altogether, this book represents an original work which differs by
many elements from the standards of analytical mechanics. As such, the
book is an important and courageous contribution which will be received
with interest among scientific community, certain statements and conclusions
being affirmed or questioned.