Foundations of Mechanics

Parts: I. Analytical Mechanics (R. Gutowski). 1. Constrained mechanical system. 2. Variational principles of mechanics. 3. Equations of motion of mechanical systems in Lagrange variables and quasi-coordinates. 4. Equations of motion of material systems in canonical variables. 5. Canonical transformations. 6. Integral invariants and conservation laws. II. Relativistic Mechanics (S.L. Bazanski). 1. Physical origin of the special theory of relativity. 2. Galilean space-time. 3. Basic space-time concepts of the special theory of relativity. 4. Minkowski space-time. 5. Relativistic kinematics. 6. Dynamics of a material point. 7. Conservation principles. 8. Equations of motion. 9. Canonical formalism. 10. Comments on the relativistic many-body problem. III. Quantum Mechanics (J. Slawianowski). 1. Basic concepts of quantum mechanics. Historical origins. 2. Quantum mechanics of a material point. Wave mechanics. 3. General formulation of quantum mechanics and examples. 4. Simple applications of quantum mechanics. 5. Some approximate methods and their applications. IV. Mechanics of Continuous Media (C. Wozniak). 1. Basic concepts. 2. Fundamental principles. 3. Investigation of the balance principles. 4. General field equations. 5. Materials. 6. Constraints and loadings. 7. Specialized theories. V. Phenomenological Thermodynamics (K. Wilmanski). 1. Introduction. 2. Fundamentals of abstract phenomenological thermodynamics. 3. Thermodynamics of thermomechanical materials. 4. Comments on the second law of thermodynamics. Bibliography. Subject Index.