CHOICE Recommended Title, June 2019
Brought together in one focused and exclusive treatment, this book provides an elementary introduction to the important role and use of the least action principle and the resulting Lagranges equations in the analysis of the laws that govern the universe. It is an ideal complimentary resource to accompany undergraduate courses and textbooks on classical mechanics.
Features:
Uses mathematics accessible to beginners Brings together the Principle of Least Action, Lagrange's equations, and variational principles in mechanics in one cohesive text Written in a clear and easy-to-understand manner
Preface |
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ix | |
Acknowledgments |
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xi | |
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1 | (6) |
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Chapter II Selected Elements of Classical and Quantum Physics |
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7 | (76) |
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8 | (17) |
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Space, Systems of Coordinates |
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9 | (4) |
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Rotation and Translation of Axes |
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13 | (4) |
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Elements of Vector Algebra |
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17 | (3) |
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Generalized Coordinates System |
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20 | (2) |
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22 | (1) |
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Velocity and Acceleration |
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23 | (1) |
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24 | (1) |
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B Universe Dynamics Using Newton's And Galileo's Principles |
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25 | (33) |
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25 | (1) |
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25 | (2) |
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27 | (1) |
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28 | (4) |
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32 | (1) |
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Inertial and Gravitational Mass |
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33 | (2) |
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35 | (2) |
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Gravitational Potential Energy |
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37 | (2) |
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39 | (1) |
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Gravity: Poisson's Equation |
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39 | (2) |
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41 | (1) |
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42 | (2) |
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Conservation of Linear Momentum |
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44 | (1) |
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Conservation of Angular Momentum |
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45 | (1) |
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46 | (1) |
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Object Sent Directly Upward in Earth's Gravitational Field |
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46 | (2) |
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Object Sent at an Angle θ Upward in Earth's Gravitational Field |
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48 | (2) |
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50 | (3) |
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53 | (5) |
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58 | (15) |
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58 | (2) |
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Special Relativity and Lorentz Transformation |
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60 | (11) |
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71 | (2) |
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D Electro-And Magneto-Dynamics |
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73 | (5) |
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73 | (4) |
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Electromagnetic Wave Equation |
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77 | (1) |
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E Quantum Physics And Electrodynamics |
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78 | (5) |
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78 | (2) |
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80 | (1) |
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Quantum Mechanics and Relativity |
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81 | (2) |
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Chapter III Search for a Universal Principle |
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83 | (30) |
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A A Mathematical Tool: Calculus Of Variations |
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85 | (12) |
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91 | (1) |
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Shortest Path on a Sphere |
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92 | (5) |
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B The Principle Of Least Action And Lagrange's Equations |
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97 | (7) |
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104 | (9) |
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Chapter IV Selected Applications of Lagrange's Equations |
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113 | (38) |
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A A Particle In Motion In A Potential |
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113 | (2) |
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115 | (6) |
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115 | (1) |
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Motion in a Plane Vertical to the Earth's Surface |
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116 | (2) |
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118 | (3) |
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121 | (1) |
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D Conservation Laws And Symmetry |
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122 | (11) |
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Conservation Of Linear Momentum |
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123 | (4) |
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Conservation Of Angular Momentum |
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127 | (3) |
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130 | (3) |
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E Hamilton's Equations Of Motion |
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133 | (2) |
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135 | (6) |
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G Universe Expansion And General Relativity |
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141 | (4) |
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145 | (6) |
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Chapter V Fields And Quantum Physics |
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151 | (12) |
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152 | (6) |
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158 | (1) |
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C A Word About Matter Waves And Quantum Mechanics |
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159 | (4) |
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163 | (4) |
References |
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167 | (2) |
Index |
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169 | |
Jacques Vanier is an adjunct professor in the Physics Department at the University of Montreal. He is a fellow of the Royal Society of Canada, the American Physical Society, and the Institute of Electrical and Electronic Engineers. He has written more than 120 journal articles and proceedings papers and is the author of several books on masers, lasers, and atomic frequency standards. He has written a book on the physics of the universe in simple language for the general public. He was professor of physics at Laval University where he gave courses on general physics. His research work is oriented toward the understanding and application of quantum electronics phenomena.
Cipriana Tomescu is an invited researcher in the Physics Department at the University of Montreal. She is the author of numerous articles in scientific journals and conference proceedings. She is the co-author with Dr. Vanier of a book on atomic frequency standards. In her career, she has worked in several institutions around the world as an invited researcher. Her research involves state-of-the-art microwave and optical atomic frequency standards.