Relativistic Mechanics, Time and Inertia

A. Aspects of Relativistic Mechanics.- A.I. General remarks.- A.II. Remarks on the theory of relativity.- A.II.1. Special relativity.- A.II.1.1. Synchronization of clocks.- A.II.1.2. The Lorentz-Einstein relations.- A.II.1.3. The invariant of Lorentz-Einstein transformations.- A.II.1.4. Classification of space-time intervals.- A.II.1.5. Minkowski space.- A.II.1.6. Transformation of velocity components.- A.II.1.7. The velocity and acceleration 4-vectors.- A.II.1.8. The momentum 4-vector.- A.II.1.9. The 4-force.- A.II.1.10. The fundamental law of dynamics and the energy of a particle in relativistic dynamics.- A.II.1.11. The momentum-energy vector and the properties of its components.- A.II.1.12. The conservative case. Potential energy.- A.II.1.13. The mass defect.- A.II.1.14. The relativistic study of collisions.- A.II.1.15. Some physical interpretations and other remarks on relativistic mechanics.- A.II.2. Some aspects of general relativity.- A.III. The main aims of this work.- B. Time.- B.I. The concept of time.- B.I.1. The evolution of the concept of time.- B.I.2. Time as measure and consequence of motion.- B.I.2.1. Motion.- B.I.2.2. The clock.- B.I.2.3. Examples of mechanical motion.- B.I.2.4. Time as an abstraction of general motion.- B.I.3. The properties of time.- B.I.3.1. The irreversibility of time.- B.I.3.2. The velocities and accelerations in various equivalence classes.- B.I.3.3. The transport of information.- B.I.3.4. Information transport as a timing motion.- B.I.3.5. The character of the unique constant velocity of light in all inertial frames.- B.I.3.6. Relativity of time and the problem of several information carriers.- B.II. Examples.- B.II.1. The irreversibility and continuity of time.- B.II.1.1. The probabilistic irreversibility.- B.II.1.2. The continuity of the time variable.- B.II.2. The forced open curves in Minkowski space.- C. Inertia.- C.I. Use of time in defining some elements of space.- C.I.1. The definition of the straight line.- C.I.1.1. Inertial spaces.- C.I.1.2. The straight line.- C.I.1.3. Non-inertial spaces.- C.I.1.4. The rigid line.- C.I.2. Reference frames.- C.I.2.1. Inertial frames.- C.I.2.2. Non-inertial frames.- C.II. The inertia.- C.II.1. Aspects related to motion of particles in inertial and non-inertial spaces.- C.II.1.1. General aspects of the study of motion in non-inertial spaces.- C.II.1.2. Mescerski-Levi-Civita equation in the relativistic case.- C.II.1.3. The effect of percussion force in the relativistic case.- C.II.2. Manifestation of inertia.- C.II.2.1. The inertial spaces.- C.II.2.2. Non-inertial spaces.- C.II.3. Some aspects of the motion of a particle in a non-inertial situation.- C.II.3.1. Accelerated translation.- C.II.3.2. A particular gravitational field.- C.II.3.3. The case of relative motion of the frame.- C.III. Some aspects of classical mechanics.- C.III.1. Grounding mechanics on a single axiom.- C.III.1.1. The single axiom of mechanics.- C.III.1.2. Definition of force and derivation of the fundamental laws of mechanics.- C.III.2. The inertial or non-inertial character of frames.- C.III.2.1. Inertial frames.- C.III.2.2. Non-inertial frames.