By week:
|
You can find the lecture notes at this link or at the Wiki.
Conserved Quantities, Center of Mass Coordinates, Virtual Work, D'Alembert's Equation, Lagrange's Equations
Lagrange's Equations and the Principle of Least Action. Cyclic
coordinates and conserved quantities.
We have covered much of these details in Week 1, but we will cover
some additional concepts (maybe even the Lorentz force equation) and
examine the two-body problem.
Let's examine how we include friction in our lovely Lagrangian
formulation.
What are the properties of the moment of inertia of a body? How do we relate
the moment of inertia about the center of mass to the inertia about another point?
We will cover the motion of rigid bodies using the Lagrangian.
This Monday (24 October 2005) is the midterm. It covers material up to 21 October 2005.
Rigid body motion using Euler angles.
Regardless of the forces involved there are general techniques to understand
small oscillations about an equilibrium state.
Let's imagine we have a system whose motion we understand by solving
the equations of motion. How does the motion change if we make a
slight change to the equations of motion or the initial conditions?
Check out the Central Force Integrator.
How can we generalize our techniques to systems with an infinite number of
degrees of freedom (fields)?
We end our tour of classical mechanics with yet another formulation that places
the momenta and coordinates on equal footing. You can find the notes for this week and
next on the Wiki.
We have two powerful approximation methods (abiabatic invariants and
impulses) that are useful when the typical timescale of the motion and
the perturbation are vastly different. We'll also look at Liouville's
theorem if we have time. You can find the notes for this week and
last on the Wiki.
Last modified: Wednesday, 30 November 2005 12:14:25
|
