Mechanical Systems, Classical Models: Volume I: Particle Mechanics

All phenomena in nature are characterized by motion; this is an essential property of matter, having infinitely many aspects. Motion can be mechanical, physical, chemical or biological, leading to various sciences of nature, mechanics being one of them. Mechanics deals with the objective laws of mechanical motion of bodies, the simplest form of motion. In the study of a science of nature mathematics plays an important role. Mechanics is the first science of nature which was expressed in terms of mathematics by considering various mathematical models, associated to phenomena of the surrounding nature. Thus, its development was influenced by the use of a strong mathematical tool; on the other hand, we must observe that mechanics also influenced the introduction and the development of many mathematical notions. In this respect, the guideline of the present book is precisely the mathematical model of mechanics. A special accent is put on the solving methodology as well as on the mathematical tools used; vectors, tensors and notions of field theory. Continuous and discontinuous phenomena, various mechanical magnitudes are presented in a unitary form by means of the theory of distributions. Some appendices give the book an autonomy with respect to other works, special previous mathematical knowledge being not necessary. Some applications connected to important phenomena of nature are presented, and this also gives one the possibility to solve problems of interest from the technical, engineering point of view. In this form, the book becomes – we dare say – a unique outline of the literature in the field; the author wishes to present the most important aspects connected with the study of mechanical systems, mechanics being regarded as a science of nature, as well as its links to other sciences of nature. Implications in technical sciences are not neglected. __Audience:__ Librarians, and researchers interested in the fundamentals of mechanics Newtonian Model of Mechanics....Pages 1-74 Mechanics of the Systems of Forces....Pages 75-114 Mass Geometry. Displacements. Constraints....Pages 115-200 Statics....Pages 201-286 Kinematics....Pages 287-351 Dynamics of the Particle with Respect to an Inertial Frame of Reference....Pages 353-400 Problems of Dynamics of the Particle....Pages 401-467 Dynamics of the Particle in a Field of Elastic Forces....Pages 469-542 Newtonian Theory of Universal Attraction....Pages 543-595 Other Considerations on Particle Dynamics....Pages 595-691 This book examines the study of mechanical systems as well as its links to other sciences of nature. It presents the fundamentals behind how mechanical theories are constructed and details the solving methodology and mathematical tools used: vectors, tensors and notions of field theory. It also offers continuous and discontinuous phenomena as well as various mechanical magnitudes in a unitary form by means of the theory of distributions. Deals with the dynamics of systems consisting of discrete particles as well as continuous systems. This book explains various important aspects of the science of mechanics, regarded as a natural science, and shows how they are useful in understanding important natural phenomena and solving problems of applied/engineering interest Vol. 1. Particle mechanics -- v. 3. Analytical mechanics