Laundry List for PH 314 Final Exam, Fall 1999

• Show that the kinetic energy of a rigid body can be expressed at the kinetic energy of the center of mass, plus the kinetic energy with respect to the center of mass.
• 1-D problems with x, v, t
• coupled oscillations -
• set up equations of motion
• determine the frequencies of oscillation
• find ration of displacements
• Lagrange's equations
• Inertia tensor - be able to calculate components of I from a given distribution of masses.
• Show that angular momentum is a constant of the motion and using a sketch that L = 2m dA/dt
• integrate over an ellipsoid to get volume, moments, principal moments of inertia
• Derive Euler's rigid body equations from dV/dt)fixed = dV/dt)rot + omega x V
• Use Euler's rigid body equations to show that rigid body motion about the intermediate axis is unstable (done in class and in book)
• coriolis force
• stability of circular motion in a force field f(r)
• frequency of oscillation near a potential minimum
• Given the lagrangian 1/2 mu (r-dot^2 + r theta-dot^2) -V(r))
• write down lagrange's equations
• determine the constants of the motion
• write down the energy in terms of an 'effective potential energy'
• series expansions
• binomial
• taylor