Аннотация
In the book the basic ideas of integrational mechanics with reference to a brief course of classical mechanics are considered. The unity of mathematics, physics and applied philosophy allows to study compactly fundamentals of classical mechanics including vibration, stability and impact. Ten problems on dynamics with the analysis of typical receptions of creativity are solved in detail. The book is intended for students and the engineers interested in studying classical mechanics in English.
Содержание
Introduction
Chapter 1. CLASSICAL MECHANICS AS A SYSTEM THEORY
1.1. Structure of the course of classical mechanics
1.2. Unity of mathematics, physics, and philosophy in Newton’s mechanics
1.3. Methods of creation in integrational mechanics
1.4. Classification of mechanics problem according to the type of nonlinearity
Chapter 2. SYSTEM APPROACH IN STATICS AND KINEMATICS
2.1. Information operator of null action and axioms of statics
2.2. System of concurrent forces
2.3. Moment of a force about a point and an axis
2.4. Reduction of two parallel forces. Couple
2.5. The basic theorem of statics
2.6. Coplanar force system. Varygnon’s theorem
2.7. Statically determinate and statically indeterminate problems
2.8. Center of gravity of bodies
2.9. Invariants of force system
2.10. Statics paradoxes
2.11. Peculiarities of kinematics as an ideal theory
2.12. Specification of a particle motion and the information compression principle
2.13. Differentiation of a vector of unit length and the analogy principle
2.14. The information operator and velocity and acceleration diagrams for a body moving with a general plane motion
2.15. Graphical method of successive analysis of velocity and acceleration in a rigid body plane motion
2.16. A system way to derive Coriolis acceleration
2.17. The analogy principle and compound rotational motions of a rigid body
Chapter 3. DYNAMICS
3.1. Newton’s laws systematization
3.2. Informational compact of Newton’s vector dynamics
3.3. The basic information compact of dynamics problems
3.4. Compact of dynamics problems (resonance)
3.5. Energy mechanics
3.6. Elements of Lagrange’s analytical mechanics
3.7. Compact «Impact phenomena in mechanics»
3.8. Compact «Linear and nonlinear problems in dynamics»
3.9. Compact «Stability»
3.10. Analytical mechanics as an «ideal» theory
3.11. System classification of forces
3.12. Classification of «physical» bodies
Chapter 4. EXAMPLES OF PROBLEM ANALYSIS
4.1. Kinematics of mass — point particle.Analogies
4.2. Dynamics of mass — point particle
4.3. Dynamics of translation motion of a system of rigid bodies
4.4. Dynamics of rotation of a system of rigid bodies
4.5. Motion of a body in potential field
4.6. Distribution of inertia forces of rigid body being in general plane motion
4.7. Bearing reactions
4.8. Differential equation of motion of a mechanism
Bibliography
