Foundations of Mechanics

The presented short course is intended as the small addendum to the imposing size classical books on the mechanics of materials. The foundations of the nonlinear, linearized, and linear theories of elasticity, as well as the strength of materials, are offered. The chapters give in brief terms the information on fundamentals of mechanics of materials and have for an object to help him to systemize of his knowledge in the area of modern mechanics of materials, to understand the common background and interdependence of models and theories of the modern mechanics of materials.

In this second volume on the Foundations of Quantum Mechanics we shall show how it is possible, using the methodology presented in Volume I, to deduce some of the most important applications of quantum mechanics. These deductions are concerned with the structures of the microsystems rather than the technical details of the construction of preparation and registration devices. Accordingly. the only new axioms (relative to Volume I) which are introduced are concerned with the relationship between ensemble operators W, effect operators F, and certain construction principles of the preparation and registration devices. The applications described here are concerned with the measurement of atomic and molecular structure and of collision experiments.

This book introduces the basic theoretical knowledge of rock mechanics and its application in petroleum engineering. It covers the gamut of the formulas and calculations for petroleum engineers that have been compiled over decades, while others are meant to help guide the engineer through some of the more recent breakthroughs in the industry’s technology.

The book presents foundations of the micropolar continuum mechanics including a short but comprehensive introduction of stress and strain measures, derivation of motion equations and discussion of the difference between Cosserat and classical (Cauchy) continua, and the discussion of more specific problems related to the constitutive modeling, i.e. constitutive inequalities, symmetry groups, acceleration waves, etc.