Universe dynamics : the least action principle and lagrange's equations / Jacques Vanier ; in collaboration with Cipriana Tomescu (Université de Montréal).
Vanier, Jacques, 1934-| Call Number | 531/.11 |
| Author | Vanier, Jacques, 1934- author. |
| Title | Universe dynamics : the least action principle and lagrange's equations / Jacques Vanier ; in collaboration with Cipriana Tomescu (Université de Montréal). |
| Physical Description | 1 online resource. |
| Contents | Cover; Half Title; Title Page; Copyright Page; Table of Contents; Preface; Acknowledgments; Chapter I. Introduction; Chapter II. Selected Elements of Classical and Quantum Physics; A. Framework; Space, Systems of Coordinates; Rotation and Translation of Axes; Elements of Vector Algebra; Generalized Coordinates System; Time; Velocity and Acceleration; Mass; B. Universe Dynamics Using Newton's and Galileo's Principles; Inertia; Force and Acceleration; Action and Reaction; Energy; Gravity; Inertial and Gravitational Mass; Gravitational Field; Gravitational Potential Energy; An Observation The Photon ConceptQuantum Mechanics and Relativity; Chapter III. Search for a Universal Principle; A. A Mathematical Tool: Calculus of Variations; Shortest Path on a Plane; Shortest Path on a Sphere; B. The Principle of Least Action and Lagrange's Equations; C. d'Alembert's Principle; Chapter IV. Selected Applications of Lagrange's Equations; A. A Particle in Motion in a Potential; B. Gravitation; Vertical Motion; Motion in a Plane Vertical to the Earth's Surface; Orbital Motion; C. The Pendulum; D. Conservation Laws and Symmetry; Conservation of Linear Momentum Conservation of Angular MomentumConservation of Energy; E. Hamilton's Equations of Motion; F. Special Relativity; G. Universe Expansion and General Relativity; H. Electromagnetic Force; Chapter V. Fields and Quantum Physics; A. Electromagnetic Field; B. Gravitational Field; C. A Word about Matter Waves and Quantum Mechanics; Chapter VI. Conclusion; References; Index |
| Summary | 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 |
| Added Author | Tomescu, Cipriana, author. |
| Subject | LEAST ACTION. LAGRANGE EQUATIONS. MECHANICS. PHYSICS. QUANTUM THEORY. SCIENCE / Mechanics / General SCIENCE / Mechanics / Solids SCIENCE / Physics SCIENCE / Mathematical Physics |
| Multimedia |
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$a The Photon ConceptQuantum Mechanics and Relativity; Chapter III. Search for a Universal Principle; A. A Mathematical Tool: Calculus of Variations; Shortest Path on a Plane; Shortest Path on a Sphere; B. The Principle of Least Action and Lagrange's Equations; C. d'Alembert's Principle; Chapter IV. Selected Applications of Lagrange's Equations; A. A Particle in Motion in a Potential; B. Gravitation; Vertical Motion; Motion in a Plane Vertical to the Earth's Surface; Orbital Motion; C. The Pendulum; D. Conservation Laws and Symmetry; Conservation of Linear Momentum
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$a Conservation of Angular MomentumConservation of Energy; E. Hamilton's Equations of Motion; F. Special Relativity; G. Universe Expansion and General Relativity; H. Electromagnetic Force; Chapter V. Fields and Quantum Physics; A. Electromagnetic Field; B. Gravitational Field; C. A Word about Matter Waves and Quantum Mechanics; Chapter VI. Conclusion; References; Index
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$a 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
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| Summary | 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 |
| Contents | Cover; Half Title; Title Page; Copyright Page; Table of Contents; Preface; Acknowledgments; Chapter I. Introduction; Chapter II. Selected Elements of Classical and Quantum Physics; A. Framework; Space, Systems of Coordinates; Rotation and Translation of Axes; Elements of Vector Algebra; Generalized Coordinates System; Time; Velocity and Acceleration; Mass; B. Universe Dynamics Using Newton's and Galileo's Principles; Inertia; Force and Acceleration; Action and Reaction; Energy; Gravity; Inertial and Gravitational Mass; Gravitational Field; Gravitational Potential Energy; An Observation The Photon ConceptQuantum Mechanics and Relativity; Chapter III. Search for a Universal Principle; A. A Mathematical Tool: Calculus of Variations; Shortest Path on a Plane; Shortest Path on a Sphere; B. The Principle of Least Action and Lagrange's Equations; C. d'Alembert's Principle; Chapter IV. Selected Applications of Lagrange's Equations; A. A Particle in Motion in a Potential; B. Gravitation; Vertical Motion; Motion in a Plane Vertical to the Earth's Surface; Orbital Motion; C. The Pendulum; D. Conservation Laws and Symmetry; Conservation of Linear Momentum Conservation of Angular MomentumConservation of Energy; E. Hamilton's Equations of Motion; F. Special Relativity; G. Universe Expansion and General Relativity; H. Electromagnetic Force; Chapter V. Fields and Quantum Physics; A. Electromagnetic Field; B. Gravitational Field; C. A Word about Matter Waves and Quantum Mechanics; Chapter VI. Conclusion; References; Index |
| Subject | LEAST ACTION. LAGRANGE EQUATIONS. MECHANICS. PHYSICS. QUANTUM THEORY. SCIENCE / Mechanics / General SCIENCE / Mechanics / Solids SCIENCE / Physics SCIENCE / Mathematical Physics |
| Multimedia |