Introduction to Lagrangian & Hamiltonian Mechanics
Publisher: Bookboon
Published: 2016
ISBN-13: 9788740312492
Table of contents: title: Fundamental principles; title: Notation and brief repetition; title: Many-particle systems; title: Constraints and generalized coordinates; title: D’Alembert’s principle and Lagrange’s equations; title: Levi-Civita symbol; title: Friction and other velocity-dependent potentials; title: Examples; title: Lagrange’s equations and the variational principle; title: Hamilton’s principle; title: Derivation of Lagrange’s equations from Hamilton’s principle; title: Variational calculus; title: Hamilton’s principle for non-holonomic systems; title: Conservation laws and symmetries; title: Hamilton’s equations; title: Legendre transformations; title: Going from Lagrangian to Hamiltonian formalism; title: The two-body problem: central forces; title: Reduction to equivalent one-body problem; title: Equations of motion; title: Equivalent one-dimensional problem; title: The virial theorem; title: The Kepler problem; title: Scattering cross section; title: Kinematics and equations of motion for rigid bodies; title: Orthogonal transformations and independent coordinates; title: Transformation matrix and its mathematical properties; title: Formal properties of the transformation matrix; title: Euler angles; title: Infinitesimal transformations; title: The rate of change of time-dependent vectors; title: Components of ! along the body axes; title: The Coriolis force; title: Angular momentum and kinetic energy; title: The Euler equations; title: Free rotation of rigid body; precession; title: Heavy symmetric top with one point fixed; title: Small-scale, coupled oscillations; title: Coupled oscillators; title: Application to a triatomic linear symmetric molecule (CO2); title: The theory of special relativity; title: Introductory remarks; title: Lorentz transformations; title: Choices of metric; title: Covariant 3+1 dimensional formulation; title: Maxwell’s equation, 4-potential, and electromagnetic field tensor; title: Relativistic mechanics and kinematics; title: The relativity of simultaneity; title: Canonical transformations; title: Transformation of phase space; title: Poisson brackets; title: Hamilton-Jacobi theory