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Introduction to Lagrangian & Hamiltonian Mechanics

Introduction to Lagrangian & Hamiltonian Mechanics
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ISBN: 978-87-403-1249-2
1 edition
Pages : 112
  • Price: 129.00 kr
  • Price: €13.99
  • Price: £13.99
  • Price: ₹250
  • Price: $13.99
  • Price: 129.00 kr
  • Price: 129.00 kr

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About the book

  1. Reviews
  2. Description
  3. Content
  4. About the Author

Reviews

Mark ★★★★★

This is what I've been looking for - easy to read with many useful examples. The Youtube videos also seem quite helpful.

Description

In both classical and quantum mechanics, the Lagrangian and Hamiltonian formalisms play a central role. They are powerful tools that can be used to analyze the behavior of a vast class of physical systems. The aim of this book is to provide an introduction to the Lagrangian and Hamiltonian formalisms in classical systems, covering both non-relativistic and relativistic systems. The lectures given in this course have been recorded on video and uploaded on YouTube. At the beginning of each chapter we provide a link to the YouTube-videos covering that particular chapter. It is our goal that students who study this material afterwards will find themselves well prepared to dig deeper into the remarkable world of theoretical physics at a more advanced level. We have carefully chosen the topics of this book to make students proficient in using and understanding important concepts such as symmetries and conservation laws, the special theory of relativity, and the Lagrange/Hamilton equations.

Content

  1. Fundamental principles
    1. Notation and brief repetition
    2. Many-particle systems
    3. Constraints and generalized coordinates
    4. D’Alembert’s principle and Lagrange’s equations
    5. Levi-Civita symbol
    6. Friction and other velocity-dependent potentials
    7. Examples
  2. Lagrange’s equations and the variational principle
    1. Hamilton’s principle
    2. Derivation of Lagrange’s equations from Hamilton’s principle
    3. Variational calculus
    4. Hamilton’s principle for non-holonomic systems
    5. Conservation laws and symmetries
  3. Hamilton’s equations
    1. Legendre transformations
    2. Going from Lagrangian to Hamiltonian formalism
  4. The two-body problem: central forces
    1. Reduction to equivalent one-body problem
    2. Equations of motion
    3. Equivalent one-dimensional problem
    4. The virial theorem
    5. The Kepler problem
    6. Scattering cross section
  5. Kinematics and equations of motion for rigid bodies
    1. Orthogonal transformations and independent coordinates
    2. Transformation matrix and its mathematical properties
    3. Formal properties of the transformation matrix
    4. Euler angles
    5. Infinitesimal transformations
    6. The rate of change of time-dependent vectors
    7. Components of ! along the body axes
    8. The Coriolis force
    9. Angular momentum and kinetic energy
    10. The Euler equations
    11. Free rotation of rigid body; precession
    12. Heavy symmetric top with one point fixed
  6. Small-scale, coupled oscillations
    1. Coupled oscillators
    2. Application to a triatomic linear symmetric molecule (CO2)
  7. The theory of special relativity
    1. Introductory remarks
    2. Lorentz transformations
    3. Choices of metric
    4. Covariant 3+1 dimensional formulation
    5. Maxwell’s equation, 4-potential, and electromagnetic field tensor
    6. Relativistic mechanics and kinematics
    7. The relativity of simultaneity
  8. Canonical transformations
    1. Transformation of phase space
    2. Poisson brackets
    3. Hamilton-Jacobi theory

About the Author

J.L. holds since 2013 a position as Professor of Physics at the Norwegian University of Science and Technology. His research is focused on theoretical quantum condensed matter physics and he has received several prizes for his Ph.D work on the interplay between superconductivity and magnetism. He has also received the American Physical Society ”Outstanding Referee” award, selected among over 60.000 active referees. In teaching courses such as Classical Mechanics and Particle Physics for both undergraduate and graduate students, he has invariably received high scores from the students for his pedagogical qualities and lectures. His webpage is found here.

I.B. has for about 20 years been a Professor of Mechanics at the Norwegian University of Science and Technology. He has worked within electrodynamics, fluid mechanics, and cosmology, and has alone or with co-authors published about 250 research papers in international journals. He was a member of the Editorial Board of Physical Review E, in the period 2009-2014, and was awarded the American Physical Society’s ”Outstanding Referee”, at their first round in 2008. The present book actually grew out from a course of lectures given by him on Classical Mechanics at the university during a period of about 15 years. His webpage is found here.

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