Later than I had planned to post,
1) Read Chapter 3.1-3.4 in your Classical Mechanics text for class on Wednesday 01/25/17
2) Watch and work through our video on quadratic drag.
3) Watch and work through our video on the Matlab Publish command.
4) Homework #3 is due 2/01/17 4pm in Jiajie Xiao's mailbox in Olin 100. It is:
A) Problems 2.15, 2.17a (no computation), 3.2 and 3.3 (use matlab for your plot) from your text
B) Using the leapfrog integrator, model throwing a ball straight up in the air with linear drag. Find the position as a function of time, and the time it takes the ball to come back to the origin. You may set the mass as 1kg, and the origin at 0, but examine what happens with a variety of initial conditions and drag coefficients. Do at least four cases: two initial velocities that vary by at least an order of magnitude with at least two different drag coefficients that vary by at least an order of magnitude. Discuss what happens as the drag changes and the initial velocity changes. Make sure to increase the number of time-steps so the time it takes for the ball to come back to x=0 converges to 1% or better.
C) Show that Euler's formula (e^(ix)=cos(x)+isin(x)) works by expanding both sides to fifth order in x and collecting terms. (It will still work if you collect all terms, but this isn't a math class.)
Note: With the exception of the computational problem and the plotting in 3.3, the problems need to be solved by hand. Using symbolic math solvers is not allowed.
5) You may want to watch our solution to problem 2.5.
6) Read or re-read Chapter 2.1.1-2.1.7 from The Mathematics Companion, for this week and for Monday. This has far more detail than we will explicitly use in class, but contains the theory behind what we will do.