An edition of Introduction to Lagrangian & Hamiltonian Mechanics
(2016)
Introduction to Lagrangian & Hamiltonian Mechanics
by Jacob Linder , Iver H. Brevik
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Last edited by Alice Kirk
March 14, 2016 | History
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.
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Publish Date
2016
Publisher
Bookboon
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Book Details
Table of Contents
Fundamental principles
Notation and brief repetition
Many-particle systems
Constraints and generalized coordinates
D’Alembert’s principle and Lagrange’s equations
Levi-Civita symbol
Friction and other velocity-dependent potentials
Examples
Lagrange’s equations and the variational principle
Hamilton’s principle
Derivation of Lagrange’s equations from Hamilton’s principle
Variational calculus
Hamilton’s principle for non-holonomic systems
Conservation laws and symmetries
Hamilton’s equations
Legendre transformations
Going from Lagrangian to Hamiltonian formalism
The two-body problem: central forces
Reduction to equivalent one-body problem
Equations of motion
Equivalent one-dimensional problem
The virial theorem
The Kepler problem
Scattering cross section
Kinematics and equations of motion for rigid bodies
Orthogonal transformations and independent coordinates
Transformation matrix and its mathematical properties
Formal properties of the transformation matrix
Euler angles
Infinitesimal transformations
The rate of change of time-dependent vectors
Components of ! along the body axes
The Coriolis force
Angular momentum and kinetic energy
The Euler equations
Free rotation of rigid body; precession
Heavy symmetric top with one point fixed
Small-scale, coupled oscillations
Coupled oscillators
Application to a triatomic linear symmetric molecule (CO2)
The theory of special relativity
Introductory remarks
Lorentz transformations
Choices of metric
Covariant 3+1 dimensional formulation
Maxwell’s equation, 4-potential, and electromagnetic field tensor
Relativistic mechanics and kinematics
The relativity of simultaneity
Canonical transformations
Transformation of phase space
Poisson brackets
Hamilton-Jacobi theory
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| March 14, 2016 | Edited by Alice Kirk | Edited without comment. |
| March 14, 2016 | Created by Alice Kirk | Added new book. |