Mechanical systems, classical models. Volume 2: Mechanics of discrete and continuous systems. Translation from the Romanian original (Q938790)

The first volume of this textbook was devoted to the dynamics of a particle [see the review in Zbl 1148.70002]. The second volume deals with mechanical systems of particles (discrete or continuous, deformable or non-deformable). It includes Chapters from 11 to 17. Dynamics of discrete mechanical systems is considered in inertial (Galilean) and non-inertial frames of reference. The cases of open and closed systems, both free and subjected to constraints, are presented. General theorems and conservation theorems are given. As one of important applications, the author discusses the problem of \(n\) particles. Then general principles and theorems are stated for dynamics of continuous mechanical systems (deformable continuous media). As applications, motions of threads and straight bars are studied. The following considerations concern discrete mechanical systems with collisions and mechanical systems of variable mass. A sizeable part of the book is devoted to the dynamics of rigid bodies. At first, general theorems are established for the motion of free and constrained rigid bodies. These results are used to study the motion of a rigid body about a fixed axis and its plane-parallel motion. One of the basic problems in the dynamics of the rigid body is the classical problem of a heavy rigid body moving about a fixed point. General methods and concrete results regarding this problem are presented thoroughly, including a large part of known cases of integrability. Another application of the dynamics of the rigid body considered in the book is the motion of the Earth in the heliocentric frame of reference. The next topic is the theory of gyroscope and its technical applications. Further, some results are presented concerning variational methods for the problem of rectilinear motion of a variable mass. The motion of the aircraft, fitted out with jet propulsion motors, is concerned too. The last topic considered in the book is the dynamics of systems of rigid bodies (free or with constraints) including the motion with discontinuities and the motion in contact with a fixed surface. The book is written clearly and rigorously, and its study does not require any special mathematical knowledge. It is intelligible and useful to a large community of scientists, engineers and students.