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Advanced Classical Mechanics

Advanced Classical Mechanics

PHYS2502 3 hours

Advanced Classical Mechanics

The course covers the study of the mechanics of rigid bodies in plane motion, in three dimensions, and their applications. Moreover, the course covers the Lagragnagian mechanics as well as a discussion of Hamilton’s equations and their applications in solving some mechanical problems.
PHYS2501 Classical Mechanics
3 hours

One requisite

Mechanics of Rigid Bodies, Planar Motion
• Center of mass of a rigid body.
• Some theorems of static equilibrium of rigid body.
• Rotation of a rigid body about a fixed axis (moment of inertia).
• Calculation of the moment of inertia. • The physical pendulum.
• General theorem concerning angular momentum.
• Laminar motion of rigid body.
Motion of Rigid Bodies in Three Dimensions
• Angular momentum of a rigid body, Products of inertia.
• Use of matrices in rigid body dynamics (the inertia tensor).
• Determination of principle axes.
• Rotational kinetic energy of a rigid body.
• Moment of inertia of a rigid body about an arbitrary axis, the momental ellipsoid.
• Euler’s equation of motion of a rigid body.
• Free rotation of a rigid body under no forces. Geometric description of the motion.
• Free rotation of a rigid body with an axis of symmetry. Analytical treatment
Lagrangian Mechanics
• Generalized coordinates.
• Generalized forces.
• Lagrange’s equations.
• Some Applications of Lagrange’s equations.
• Generalized moments ignorable coordinate.
• Lagrange’s equations for impulsive forces.
• Hamilton’s variational principle. • The Hamiltonian function (Hamiltonian equation).