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El. knyga: Conceptual Evolution of Newtonian and Relativistic Mechanics

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This book provides an introduction to Newtonian and relativistic mechanics. Unlike other books on the topic, which generally take a 'top-down' approach, it follows a novel system to show how the concepts of the 'science of motion' evolved through a veritable jungle of intermediate ideas and concepts. Starting with Aristotelian philosophy, the text gradually unravels how the human mind slowly progressed towards the fundamental ideas of inertia physics. The concepts that now appear so obvious to even a high school student took great intellectuals more than a millennium to clarify. The book explores the evolution of these concepts through the history of science. After a comprehensive overview of the discovery of dynamics, it explores fundamental issues of the properties of space and time and their relation with the laws of motion. It also explores the concepts of spatio-temporal locality and fields, and offers a philosophical discussion of relative motion versus absolute motion, as well as the concept of an absolute space. Furthermore, it presents Galilean transformation and the principle of relativity, inadequacy of Galilean relativity and emergence of the spatial theory of relativity with an emphasis on physical understanding, as well as the debate over relative motion versus absolute motion and Mach's principle followed by the principle of equivalence. The natural follow-on to this section is the physical foundations of general theory of relativity. Lastly, the book ends with some new issues and possibilities regarding further modifications of the laws of motion leading to the solution of a number of fundamental issues closely connected with the characteristics of the cosmos. It is a valuable resource for undergraduate students of physics, engineering, mathematics, and related disciplines. It is also suitable for interdisciplinary coursework and introductory reading outside the classroom.

1 Evolution of Dynamics
1(46)
1.1 Early Concepts and Aristotelian Physics
1(3)
1.1.1 The Earth
2(1)
1.1.2 Earth-Moon Distance
2(1)
1.1.3 Measuring the Sun's Distance
2(1)
1.1.4 Size of the Universe
2(2)
1.2 Role of Astronomy
4(1)
1.3 Difficulties in Discovering the Laws of Motion
5(1)
1.4 Pre-copernican Astronomy
5(7)
1.4.1 Hipparchus
5(1)
1.4.2 The Epicycle-Deferent Model and Ptolemy
6(4)
1.4.3 Problems with Explaining the Observations with Ptolemaic Model
10(1)
1.4.4 Progress During the Period Between Ptolemy and Copernicus
11(1)
1.5 Copernican Model: Rediscovery of the Heliocentric Theory
12(2)
1.6 Tycho Brahe: Improvement in Accuracy for Naked-Eye Astronomy
14(1)
1.7 Kepler: Beginning of Modern Astronomy and Foundation of Science of Motion
14(6)
1.7.1 Discovery of the Laws of Planetary Motion
15(4)
1.7.2 Transition from Geometric to Physical Model
19(1)
1.7.3 Early Concept of Action-at-a-Distance and Gravitation, and the Concept of Force
19(1)
1.8 Galileo: Naked Eye to Telescopic Astronomy
20(2)
1.8.1 Observation of the Moon and Discarding the Concept of Fifth Element
20(1)
1.8.2 Discovery of Jupiter's Moons and its Implications
21(1)
1.8.3 Discovery of the Phases of Venus: A Further Proof of Heliocentric Model
21(1)
1.9 Galileo: Experimental Mechanics
22(5)
1.9.1 Early Works on Accelerated Change: Merton School
23(1)
1.9.2 Galileo's Work on Free Fall and Uniformly Accelerated Motion
23(2)
1.9.3 Discovery of the Law of Inertia of Motion in Its Primitive Form
25(1)
1.9.4 Laws of Compound Motion: Projectiles
25(2)
1.9.5 Galilean Relativity
27(1)
1.10 Collapse of the Old Science
27(1)
1.11 Descartes: Beginning of Inertial Science
28(2)
1.11.1 Law of Inertia of Motion
28(1)
1.11.2 Collision Problems and Early Concept of Momentum Conservation
29(1)
1.11.3 Descartes' Concept of Motion
29(1)
1.12 Huygens: Breakthrough in the Discovery of Dynamics
30(6)
1.12.1 Theory of Collision and Conservation of Momentum
30(2)
1.12.2 Kinematics of Circular Motion and `Centrifugal Force'
32(2)
1.12.3 Modem Concept of Force and the `Force-Acceleration' Relation: Second Law of Motion in Primitive Form
34(1)
1.12.4 Early Concept of the Principle of Equivalence
35(1)
1.13 Halley, Wren and Hooke: Rudiments of Gravitation
36(1)
1.14 Newton and the Final Synthesis
37(7)
1.14.1 Concepts of Mass, Momentum, Force and the Second Law of Motion
37(1)
1.14.2 Collision Problem and the Discovery of the Third Law
38(1)
1.14.3 Law of Universal Gravitation and Planetary Motion
39(2)
1.14.4 Universality of Gravitational Force
41(1)
1.14.5 Orbit for Inverse Square Law
42(2)
1.15 Newtonian Dynamics in Matured State
44(3)
1.15.1 Concept of Mass
45(1)
1.15.2 Principia and Subsequent Development
45(2)
2 Some Basic Concepts in Newtonian Mechanics
47(28)
2.1 Nature of Motion and Space
47(6)
2.1.1 Newton's Concept of Absolute Space and Time
47(1)
2.1.2 Newton's Bucket Experiment
48(1)
2.1.3 Newton's Bucket Experiment Follow up
49(1)
2.1.4 Ernst Mach and Mach's Principle
50(1)
2.1.5 Quantification of Mach's Principle---Concept of Inertial Induction
50(2)
2.1.6 Origin of Inertia
52(1)
2.2 Relative--Absolute Duality of Nature of Motion
53(2)
2.2.1 The Nature of the Universe
53(1)
2.2.2 Absolute Motion in Terms of Relative Motion
53(2)
2.3 Inertial and Gravitational Mass
55(3)
2.3.1 Inertial Mass
56(1)
2.3.2 Gravitational Mass
56(1)
2.3.3 Equivalence of Inertial and Gravitational Mass
57(1)
2.4 Space--Time and Symmetry in Newtonian Mechanics
58(1)
2.5 Early Concept of Energy
59(1)
2.6 The Principle of Relativity and Galilean Transformation
60(6)
2.6.1 The Principle of Relativity
61(1)
2.6.2 Symmetry and Relativity
62(1)
2.6.3 Form Invariance of Physical Laws
63(1)
2.6.4 Energy and Energy Function
64(1)
2.6.5 Energy Function
65(1)
2.7 Laws of Motion and the Properties of Space and Time
66(4)
2.7.1 The Second Law of Motion
67(1)
2.7.2 The Third Law of Motion
68(2)
2.8 Action-at-a-Distance and Spatiotemporal Locality
70(5)
2.8.1 Early Work on Non-contact Forces
70(1)
2.8.2 Spatiotemporal Locality and Action-at-a-Distance
71(1)
2.8.3 The Concept of Field
71(3)
2.8.4 Field and Absolute Space
74(1)
3 Post `Principia' Developments
75(12)
3.1 Early Concepts and Aristotelian Physics
75(3)
3.1.1 Diffusion of Newton's Mechanics in Europe
75(1)
3.1.2 Multiplicity in the Concept of Force
76(1)
3.1.3 Degeometrization of Newtonian Mechanics
76(2)
3.2 Emergence of Analytical Mechanics
78(6)
3.2.1 New Principles for Dynamical Problems
79(1)
3.2.2 Principle of Virtual Velocity and Virtual Work
79(2)
3.2.3 D'Alembert's Principle
81(1)
3.2.4 Principle of Least Action
82(1)
3.2.5 Lagrangian Mechanics
83(1)
3.3 Dynamics of Rigid Bodies
84(3)
4 Special Theory of Relativity
87(16)
4.1 Introduction
87(1)
4.1.1 Space--Time in Newtonian Mechanics
87(1)
4.2 Euler's Work on Relativity: Confrontation of Dynamics with Optics
88(3)
4.2.1 Principle of Relativity in Solving Rigid Body Dynamics Problem
88(1)
4.2.2 Euler's Work on the Problem of Stellar Aberration
88(3)
4.3 Efforts to Detect Ether Speed: The Null Result of Michelson--Morley Experiment
91(2)
4.3.1 Early Attempts
91(1)
4.3.2 Michelson--Morley Experiment
92(1)
4.4 Electromagnetism: Challenge to the Principle of Relativity
93(3)
4.5 Einstein's Special Theory of Relativity
96(7)
4.5.1 Lorentz's Transformation from the Two Principles of Relativity
97(1)
4.5.2 Special Relativity in Electromagnetic Phenomenon
98(2)
4.5.3 Need for a Relativistic Mechanics
100(3)
5 General Theory of Relativity and Extension of Mach's Principle
103(14)
5.1 Introduction
103(1)
5.2 Transition to General Relativity
104(7)
5.2.1 Minkowski's Four-Dimensional Space--Time Continuum
104(1)
5.2.2 Principle of Equivalence
105(1)
5.2.3 Freely Falling Frames
106(3)
5.2.4 Uniformly Accelerating Frames and the `Entwurf' Theory
109(1)
5.2.5 The Field Equation and Final Formulation
110(1)
5.3 Extension of Mach's Principle
111(6)
5.3.1 Velocity-Dependent Inertial Induction
112(2)
5.3.2 Some Features of Velocity-Dependent Inertial Induction
114(1)
5.3.3 Concluding Remarks
115(2)
Bibliography 117(2)
Index 119
Amitabha Ghosh completed his bachelors, masters and doctoral degrees in Mechanical Engineering at Calcutta University in 1962, 1964 and 1969 respectively. After serving as a lecturer in Mechanical Engineering at his alma mater, Bengal Engineering College, Shibpur (now an Institute of National Importance Indian Institute of Engineering Science and Technology, Shibpur) from 1965 to 1970, Professor Ghosh joined the Indian Institute of Technology Kanpur in January 1971 as an assistant professor and served as Professor of Mechanical Engineering there from June 1975 till his retirement in 2006.  From 1977 to 1978, Professor Ghosh was Senior Fellow of the Alexander von Humboldt Foundation at the RWTH Aachen and subsequently visited the university with a Humboldt fellowship many more times. He was director of the Indian Institute of Technology Kharagpur from 1997 to 2002. His primary areas of research are manufacturing science, robotics, kinematics and mechanism theory, and dynamics of mechanical systems. Professor Ghosh has written a number of textbooks, which are popular, both in India and abroad. He has guided numerous masters and doctoral students and published a large number of research papers. He received several academic awards, including a number of Calcutta University Gold Medals, D Sc (h.c.), distinguished teacher award from IIT Kanpur and an award for excellence in research from the National Academy of Engineering. He is a fellow of all four national science and engineering academies in India.
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