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E-raamat: Lagrangian and Hamiltonian Analytical Mechanics: Forty Exercises Resolved and Explained

  • Formaat: EPUB+DRM
  • Sari: UNITEXT for Physics
  • Ilmumisaeg: 23-Nov-2018
  • Kirjastus: Springer Verlag, Singapore
  • Keel: eng
  • ISBN-13: 9789811330261
  • Formaat - EPUB+DRM
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  • Formaat: EPUB+DRM
  • Sari: UNITEXT for Physics
  • Ilmumisaeg: 23-Nov-2018
  • Kirjastus: Springer Verlag, Singapore
  • Keel: eng
  • ISBN-13: 9789811330261

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This textbook introduces readers to the detailed and methodical resolution of classical and more recent problems in analytical mechanics. This valuable learning tool includes worked examples and 40 exercises with step-by-step solutions, carefully chosen for their importance in classical, celestial and quantum mechanics. 

The collection comprises six chapters, offering essential exercises on: (1) Lagrange Equations; (2) Hamilton Equations; (3) the First Integral and Variational Principle; (4) Canonical Transformations; (5) Hamilton – Jacobi Equations; and (6) Phase Integral and Angular Frequencies

Each chapter begins with a brief theoretical review before presenting the clearly solved exercises. The last two chapters are of particular interest, because of the importance and flexibility of the Hamilton-Jacobi method in solving many mechanical problems in classical mechanics, as well as quantum and celestial mechanics.

Above all, the book provides students and teachers alike with detailed, point-by-point and step-by-step solutions of exercises in Lagrangian and Hamiltonian mechanics, which are central to most problems in classical physics, astronomy, celestial mechanics and quantum physics.

1 Lagrange Equations
1(18)
1.1 Reminder
2(3)
1.1.1 Generalized Coordinates
2(1)
1.1.2 Kinetic Energy
2(1)
1.1.3 Generalized Forces
2(1)
1.1.4 Lagrange Equations
3(1)
1.1.5 Generalized Moment
3(1)
1.1.6 Lagrange Equations for Systems with Constraints
4(1)
1.1.7 Lagrange Equations with Impulse Forces
4(1)
1.2 Exercises
5(14)
1.2.1 Exercise 1: Double Pendulum
5(2)
1.2.2 Exercise 2: Particle on a Paraboloid
7(2)
1.2.3 Exercise 3: Sphere Rolling on Another Sphere
9(3)
1.2.4 Exercise 4: Truck Descending a Slope
12(4)
1.2.5 Exercise 5: Sliding and Rotating Masses
16(3)
2 Hamilton Equations
19(6)
2.1 Reminder
20(1)
2.1.1 Hamiltonian
20(1)
2.1.2 Hamilton Equations
20(1)
2.1.3 Conservative System
20(1)
2.1.4 Expression of the Hamiltonian in Different Coordinate Systems
21(1)
2.2 Exercises
21(4)
2.2.1 Exercise 6: Particle in a Plane with Central Force
21(2)
2.2.2 Exercise 7: Harmonic Oscillator
23(2)
3 First Integral and Variational Principle
25(14)
3.1 Reminder
25(3)
3.1.1 Cyclic Coordinate
25(1)
3.1.2 Poisson Brackets
25(1)
3.1.3 Theorem of Poisson
26(1)
3.1.4 Euler Equation
27(1)
3.1.5 Variational Principle
27(1)
3.1.6 Application in Optics: Fermat Principle
27(1)
3.2 Exercises
28(11)
3.2.1 Exercise 8: Watt Regulator
28(1)
3.2.2 Exercise 9: First Integral of a Free Material Point
29(1)
3.2.3 Exercise 10: Brachistochrone Problem
30(3)
3.2.4 Exercise 11: Minimum Surface of Revolution
33(2)
3.2.5 Exercise 12: Optical Path and Fermat Principle
35(4)
4 Canonical Transformations or Contact Transformations
39(12)
4.1 Reminder
39(2)
4.1.1 Canonical Transformations
39(1)
4.1.2 Condition for a Transformation to be Canonical
40(1)
4.1.3 Generating Functions
40(1)
4.2 Exercises
41(10)
4.2.1 Exercise 13: Canonical Transformation 1
41(3)
4.2.2 Exercise 14: Canonical Transformation 2
44(1)
4.2.3 Exercise 15: Canonical Transformation 3
44(1)
4.2.4 Exercise 16: Canonical Transformation 4
45(1)
4.2.5 Exercise 17: Canonical Transformation 5
45(1)
4.2.6 Exercise 18: Canonical Transformation 6
46(1)
4.2.7 Exercise 19: Canonical Transformation 7
47(1)
4.2.8 Exercise 20: Canonical Transformation 8 and Harmonic Oscillator 2
48(3)
5 Hamilton--Jacobi Equations
51(40)
5.1 Reminder
51(2)
5.1.1 Hamilton--Jacobi Equations
51(1)
5.1.2 Solution of Hamilton--Jacobi Equations
52(1)
5.1.3 Time Independent Hamiltonian
52(1)
5.2 Exercises
53(38)
5.2.1 Exercise 21: Harmonic Oscillator 3
53(2)
5.2.2 Exercise 22: Free Falling Particle
55(2)
5.2.3 Exercise 23: Ballistic Flight of a Projectile
57(3)
5.2.4 Exercise 24: Particle Sliding on an Inclined Plane
60(2)
5.2.5 Exercise 25: Connected Particles Sliding on Inclined Surfaces
62(2)
5.2.6 Exercise 26: Unconventional Mechanics
64(2)
5.2.7 Exercise 27: Double Pendulum 2
66(2)
5.2.8 Exercise 28: Classical Problem of Kepler
68(5)
5.2.9 Additional Note on the Classical Problem of Kepler
73(1)
5.2.10 Exercise 29: Particle and Potential in --- Kcosθ/r2
74(3)
5.2.11 Exercise 30: Schrodinger Equation
77(2)
5.2.12 Exercise 31: Stark Effect
79(7)
5.2.13 Exercise 32: Particle in a Double Coulomb Field
86(3)
5.2.14 Exercise 33: Particle in Coulomb and Uniform Fields
89(2)
6 Phase Integral and Action-Angle Variables
91(34)
6.1 Reminder
91(1)
6.1.1 Phase Integral
91(1)
6.1.2 Frequency and Angular Variable
92(1)
6.2 Exercises
92(33)
6.2.1 Exercise 34: Harmonic Oscillator 4
92(1)
6.2.2 Exercise 35: Small Oscillations of the Pendulum
93(8)
6.2.3 Exercise 36: Three Dimension Harmonic Oscillator
101(4)
6.2.4 Exercise 37: Energy in a Bohr Atom
105(4)
6.2.5 Exercise 38: Classical Kepler Problem 2
109(5)
6.2.6 Exercise 39: Relativistic Kepler Problem
114(4)
6.2.7 Exercise 40: Advance of Mercury Perihelion
118(7)
Selected Bibliography 125(2)
Index 127
Vladimir Pletser earned his M. Eng. in Mechanics in 1979, M.Sc. in Geophysics in 1980 and a Ph.D. in Astrophysics in 1990, all at the University of Louvain, Belgium. Since 2018, he is Director for Space Training Operations at Blue Abyss, a company based in the United Kingdom and proposing a new approach for astronaut training. From 2016 till 2018, he has been a visiting professor scientific adviser at the Chinese Academy of Sciences in Beijings Technology and Engineering Centre for Space Utilization, supporting the preparation and development of microgravity research instrumentation for parabolic flights and for the future Chinese Space Station. He previously worked for 30 years as a senior physicist engineer at the European Space Research and Technology Centre (ESTEC) of the European Space Agency (ESA), where he was in charge of developing scientific instruments for microgravity research in fluid physics, crystallisation of proteins and zeolites and on dexterous manipulation on board the International Space Station. At ESA he was also responsible for the aircraft parabolic flight microgravity research programme and he logged more than 7350 parabolas, representing almost 40 hours of weightlessness, equivalent to 26 Earth orbits, and 53 min and 50 min at Mars and Moon g levels, during which he participated in several hundred experiments in physical and life sciences. He holds the official Guinness World Record for the number of airplanes (12) on which he has flown parabolas. He was a flight instructor for public for discovery parabolic flights. An astronaut candidate for Belgium since 1991, he was payload specialist candidate for several spacelab missions, including Spacelab LMS for which he spent two months in training at NASA-JSC, Houston in 1995. He was an astronaut training instructor for parabolic flights for ESA astronauts and for NASA and DLR astronauts for several spacelab missions.In 2001, he was selected by The Mars Society, a private organisation promoting the human exploration of Mars, to participate in three international Mars mission simulations: in the Arctic Circle in 2001 and in the Desert of Utah in 2002 and as crew commander in 2009. He is visiting professor at 20 universities in Europe, USA, Canada, Africa, Israel, and China. He has more than 600 publications, including 13 books and book chapters, 60 articles in refereed journals and 130 articles in international conferences proceedings. He has given more than 600 presentations and conferences. He is a member of the International Astronautical Academy and of several other academies and scientific organisations.