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E-raamat: Universe Dynamics: The Least Action Principle and Lagranges Equations [Taylor & Francis e-raamat]

(Université de Montréal, Quebec, Canada), (Université de Montréal, Quebec, Canada)
  • Formaat: 172 pages, 36 Line drawings, black and white; 36 Illustrations, black and white
  • Ilmumisaeg: 22-Jan-2019
  • Kirjastus: CRC Press
  • ISBN-13: 9780429443473
Teised raamatud teemal:
  • Taylor & Francis e-raamat
  • Hind: 327,75 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
  • Tavahind: 468,21 €
  • Säästad 30%
  • Formaat: 172 pages, 36 Line drawings, black and white; 36 Illustrations, black and white
  • Ilmumisaeg: 22-Jan-2019
  • Kirjastus: CRC Press
  • ISBN-13: 9780429443473
Teised raamatud teemal:
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 ix
Acknowledgments xi
Chapter I Introduction
1(6)
Chapter II Selected Elements of Classical and Quantum Physics
7(76)
A Framework
8(17)
Space, Systems of Coordinates
9(4)
Rotation and Translation of Axes
13(4)
Elements of Vector Algebra
17(3)
Generalized Coordinates System
20(2)
Time
22(1)
Velocity and Acceleration
23(1)
Mass
24(1)
B Universe Dynamics Using Newton's And Galileo's Principles
25(33)
Inertia
25(1)
Force and Acceleration
25(2)
Action and Reaction
27(1)
Energy
28(4)
Gravity
32(1)
Inertial and Gravitational Mass
33(2)
Gravitational Field
35(2)
Gravitational Potential Energy
37(2)
An Observation
39(1)
Gravity: Poisson's Equation
39(2)
Conservation Principles
41(1)
Conservation of Energy
42(2)
Conservation of Linear Momentum
44(1)
Conservation of Angular Momentum
45(1)
Illustrative Examples
46(1)
Object Sent Directly Upward in Earth's Gravitational Field
46(2)
Object Sent at an Angle θ Upward in Earth's Gravitational Field
48(2)
The Simple Pendulum
50(3)
Orbital Motion
53(5)
C Relativity
58(15)
Moving Reference Frames
58(2)
Special Relativity and Lorentz Transformation
60(11)
General Relativity
71(2)
D Electro-And Magneto-Dynamics
73(5)
Maxwell's Equations
73(4)
Electromagnetic Wave Equation
77(1)
E Quantum Physics And Electrodynamics
78(5)
Schrodinger's Equation
78(2)
The Photon Concept
80(1)
Quantum Mechanics and Relativity
81(2)
Chapter III Search for a Universal Principle
83(30)
A A Mathematical Tool: Calculus Of Variations
85(12)
Shortest Path on a Plane
91(1)
Shortest Path on a Sphere
92(5)
B The Principle Of Least Action And Lagrange's Equations
97(7)
C D'alembert's Principle
104(9)
Chapter IV Selected Applications of Lagrange's Equations
113(38)
A A Particle In Motion In A Potential
113(2)
B Gravitation
115(6)
Vertical Motion
115(1)
Motion in a Plane Vertical to the Earth's Surface
116(2)
Orbital Motion
118(3)
C The Pendulum
121(1)
D Conservation Laws And Symmetry
122(11)
Conservation Of Linear Momentum
123(4)
Conservation Of Angular Momentum
127(3)
Conservation Of Energy
130(3)
E Hamilton's Equations Of Motion
133(2)
F Special Relativity
135(6)
G Universe Expansion And General Relativity
141(4)
H Electromagnetic Force
145(6)
Chapter V Fields And Quantum Physics
151(12)
A Electromagnetic Field
152(6)
B Gravitational Field
158(1)
C A Word About Matter Waves And Quantum Mechanics
159(4)
Chapter VI Conclusion
163(4)
References 167(2)
Index 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.