Universe dynamics: the least action principle and Lagrange's equations
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press, Taylor & Francis Group
[2019]
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | xi, 172 Seiten Illustrationen |
| ISBN: | 9781138335790 1138335797 1138335894 9781138335899 |
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Record in the Search Index
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| adam_text | Contents Preface, ix Acknowledgments, xi Chapter I Chapter II A. B. ■ Introduction ■ Selected Elements of Classical and Quantum Physics FRAMEWORK 1 7 8 Space, Systems of Coordinates Rotation and Translation of Axes Elements of Vector Algebra Generalized Coordinates System Time Velocity and Acceleration Mass 9 13 17 20 22 23 24 UNIVERSE DYNAMICS USING NEWTON S AND GALILEO S PRINCIPLES 25 Inertia Force and Acceleration Action and Reaction Energy Gravity Inertial and Gravitational Mass Gravitational Field Gravitational Potential Energy 25 25 27 28 32 33 35 37 An Observation 39
vi ■ Contents Gravity: Poisson’s Equation Conservation Principles Conservation of Energy Conservation of Linear Momentum Conservation of Angular Momentum Illustrative Examples Object Sent Directly Upward in Earth’s Gravitational Field Object Sent at an Angle Θ Upward in Earth’s Gravitational Field The Simple Pendulum Orbital Motion C. D. E. B. C. 42 44 45 46 46 48 50 53 RELATIVITY 58 Moving Reference Frames Special Relativity and Lorentz Transformation General Relativity 58 60 71 ELECTRO-AND MAGNETO-DYNAMICS 73 Maxwell’s Equations Electromagnetic Wave Equation 73 77 QUANTUM PHYSICS AND ELECTRODYNAMICS 78 Schrödinger’s Equation The Photon Concept Quantum Mechanics and Relativity 78 80 81 Chapter A. 39 41 III ■ Search for a Universal Principle____________ J53 A MATHEMATICAL TOOL: CALCULUS OF VARIATIONS 85 Shortest Path on a Plane Shortest Path on a Sphere 91 92 THE PRINCIPLE OF LEAST ACTION AND LAGRANGE S EQUATIONS 97 D ALEMBERT S PRINCIPLE 104
Contents ■ vii Chapter IV ■ Selected Applications of Lagrange s Equations 113 A. A PARTICLE IN MOTION IN A POTENTIAL 113 B. GRAVITATION 115 Vertical Motion Motion in a Plane Vertical to the Earth’s Surface Orbital Motion 115 116 118 C. THE PENDULUM 121 D. CONSERVATION LAWS AND SYMMETRY 122 Conservation of Linear Momentum Conservation of Angular Momentum Conservation of Energy 123 127 130 E. HAMILTON S EQUATIONS OF MOTION 133 F. SPECIAL RELATIVITY 135 G. UNIVERSE EXPANSION AND GENERAL RELATIVITY 141 H. ELECTROMAGNETIC FORCE 145 Chapter V · Fields and Quantum Physics 151 A. ELECTROMAGNETIC FIELD 152 B. GRAVITATIONAL FIELD 158 C. A WORD ABOUT MATTER WAVES AND QUANTUM MECHANICS 159 Chapter VI · Conclusion REFERENCES, 167 INDEX, 169 163
UNIVERSE DYNAMICS 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 Lagrange s 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 About the Authors Jacques Vanier is an adjunct professor In the Physics Department at the Uni֊ versity 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 Uni versity of Montreal. She is the author of numerous articles in scientific journals and conference proceedings. She is the co-author with J. 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. PHYSICS CRC Press Taylor 6* kancis Croup an informa business www.crcpress.com CRC Press titles aro available as eBook editions in a range of digital formats ISBN: 47Տ-1-13Ս-33574-Ս 978113833579090000
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| author | Vanier, Jacques 1934- Tomescu, Cipriana |
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| physical | xi, 172 Seiten Illustrationen |
| publishDate | 2019 |
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| spelling | Vanier, Jacques 1934- Verfasser (DE-588)1184631395 aut Universe dynamics the least action principle and Lagrange's equations Jacques Vanier in collaboration with Cipriana Tomescu Boca Raton ; London ; New York CRC Press, Taylor & Francis Group [2019] xi, 172 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Lagrange-Gleichungen (DE-588)4166461-9 gnd rswk-swf Theoretische Mechanik (DE-588)4185100-6 gnd rswk-swf Prinzip der kleinsten Wirkung (DE-588)4229778-3 gnd rswk-swf Mechanik (DE-588)4038168-7 gnd rswk-swf Hamiltonsches Prinzip (DE-588)4158958-0 gnd rswk-swf Lagrange-Bewegungsgleichungen (DE-588)4166460-7 gnd rswk-swf Variationsprinzip (DE-588)4062354-3 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Least action Lagrange equations Mechanics Physics Quantum theory Hamiltonsches Prinzip (DE-588)4158958-0 s Lagrange-Bewegungsgleichungen (DE-588)4166460-7 s Lagrange-Gleichungen (DE-588)4166461-9 s Mechanik (DE-588)4038168-7 s Prinzip der kleinsten Wirkung (DE-588)4229778-3 s Quantenmechanik (DE-588)4047989-4 s Theoretische Mechanik (DE-588)4185100-6 s Variationsprinzip (DE-588)4062354-3 s DE-604 Tomescu, Cipriana Verfasser aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031255126&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031255126&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Vanier, Jacques 1934- Tomescu, Cipriana Universe dynamics the least action principle and Lagrange's equations Lagrange-Gleichungen (DE-588)4166461-9 gnd Theoretische Mechanik (DE-588)4185100-6 gnd Prinzip der kleinsten Wirkung (DE-588)4229778-3 gnd Mechanik (DE-588)4038168-7 gnd Hamiltonsches Prinzip (DE-588)4158958-0 gnd Lagrange-Bewegungsgleichungen (DE-588)4166460-7 gnd Variationsprinzip (DE-588)4062354-3 gnd Quantenmechanik (DE-588)4047989-4 gnd |
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| title | Universe dynamics the least action principle and Lagrange's equations |
| title_auth | Universe dynamics the least action principle and Lagrange's equations |
| title_exact_search | Universe dynamics the least action principle and Lagrange's equations |
| title_full | Universe dynamics the least action principle and Lagrange's equations Jacques Vanier in collaboration with Cipriana Tomescu |
| title_fullStr | Universe dynamics the least action principle and Lagrange's equations Jacques Vanier in collaboration with Cipriana Tomescu |
| title_full_unstemmed | Universe dynamics the least action principle and Lagrange's equations Jacques Vanier in collaboration with Cipriana Tomescu |
| title_short | Universe dynamics |
| title_sort | universe dynamics the least action principle and lagrange s equations |
| title_sub | the least action principle and Lagrange's equations |
| topic | Lagrange-Gleichungen (DE-588)4166461-9 gnd Theoretische Mechanik (DE-588)4185100-6 gnd Prinzip der kleinsten Wirkung (DE-588)4229778-3 gnd Mechanik (DE-588)4038168-7 gnd Hamiltonsches Prinzip (DE-588)4158958-0 gnd Lagrange-Bewegungsgleichungen (DE-588)4166460-7 gnd Variationsprinzip (DE-588)4062354-3 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Lagrange-Gleichungen Theoretische Mechanik Prinzip der kleinsten Wirkung Mechanik Hamiltonsches Prinzip Lagrange-Bewegungsgleichungen Variationsprinzip Quantenmechanik |
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