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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).

## 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.