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Classical Mechanics: Course Outline

In physics, classical mechanics and quantum mechanics are the two major sub-fields of mechanics. Classical mechanics is concerned with the set of physical laws describing the motion of bodies under the influence of a system of forces.

Course Outline

  • Survey of the elementary principles.
  • Mechanics of a particle.
  • Mechanics of a system of particles.
  • Constraint, D' Alembert's principle and Lagrange's equations.
  • Velocity-dependent potentials and the principle dissipation function.
  • Simple applications of the Lagrangian formulation.
  • Variational principles and Lagrange's equations.
  • Hamilton's principle.
  • Some techniques of the calculus of variations.
  • Derivation of Lagrange's equations from Hamilton's principle.
  • Extension of Hamilton's to Nonholonomic systems.
  • Advantages of a variational principle formulation.
  • Conservation theorems and symmetry properties.
  • Conservation theorems and symmetry properties.
  • Energy function and the conservation of energy.
  • The central force problem.
  • Reduction to the equivalent one-body problem.
  • The equations of motion and first integrals.
  • The equivalent one-dimensional problem, and Classification of orbits.
  • The virial theorem.
  • The differential equation for the orbit, and Integrable power-law potentials.
  • Conditions for closed orbits (Bertrand's theorem).

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Course Outline

  • The Kepler problem: Inverse-square law of force.
  • The motion in time in the Kepler problem.
  • The Laplace-Runge-Lenz Vector.
  • Scattering in a central force field.
  • Transformation of the scattering problem to laboratory coordinates.
  • The three-body problem.
  • The Rigid Body Equations Of Motion.
  • Angular momentum and kinetic energy ot motion about a point.
  • Tensors.
  • The inertia tensor and the moment of inertia.
  • The Eigenvalues of the inertia tensor and the principal axis transformation.
  • Solving rigid body problems and the Euler equations of motion.
  • Torque-free motion of a rigid body.
  • The heavy symmetrical top with one point fixed.
  • Precession of the equinoxes and of satellite orbits.
  • Precession of systems of charges in a magnetic field.
  • The Hamilton Equations Of Motion.
  • Legendre transformations and the Hamilton equations of motion.
  • Cyclic coordinates and conservation theorems.
  • Routh's procedure.
  • The Hamiltonian formulation of relativistic mechanics.
  • Derivation of Hamilton's equations from a variation principle.
  • The principle of least action.