Priority Items for Final Exam PH 314 Fall 2002                                                       11/09/02

• Write Lagrange's equations for a  system and solve for equations of motion
• masses and springs
• 2-body problem
• others
• Rigid body motion
• Show that dV/dt(fixed frame) = dV/dt(rotating frame) + omega x V
• Write down Euler's equations in the body-centered frame (section 11.8)
• Wobble of Earth angular velocity vector (sect 11.9)
• Derive the Stability theorem: instability about intermediate axis of rotation (section 11.11)
• Euler's angles theta, phi, psi to orient a rigid body in space (sects11.7, 11.10)
• Find the Lagrangian for a system, then write the Hamiltonian. Write Hamilton's equations. (sect 7.10)
• Force as a 1-D function of
• position
• velocity
• time
• find velocity and postion
• Stability of small oscillations about a circular orbit, given a force as a function of r (2-body problem)
• Solve a stability problem using the effective potential (V(r)  in terms of angular momentum (sect. 8.6))
• Given V(x) and mass m in the potential, find the frequency of small oscillations about a min in V
• Coupled oscillations - 2 degrees of freedom
• write out the equations
• find the two 'normal mode' frequencies
• find the ratio of amplitudes for each frequency
• Start from sum of forces = ma in an inertial system and derive f = ma in a rotating coordinate system
• (This will give pseudo-forces including coriolis and centrifugal forces)
• Derive the rotation matrix to go from vector components before and after a single rotation (needs a sketch)
• Derive the similarity transform for the inertia tensor when axes are rotated
• No stuff on Q of damped oscillator, or damped oscillator, or driven oscillator