Homework #8, due Tuesday 11/24/98.

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(1) Turn in your complete and correct ODE model for the twirling baton.

(2) Consider this innocuous-looking system: <img align=top src=lorenz.gif>.

(a) Use lsoda to approximate the solution of the initial value problem
    x0=5, y0=5, z0=5, with the parameters set at r=28, s=10, b=8/3.
    Let your initial step-size be .01, and let t run from 0 to 30, or longer.
    Make a yz-plot of your solution, using a plotting program of your choice.
    If you don't know of any, you may use the following (on ubunix or math):

	cp ~ringland/plot_descr_1.dat .
	~ringland/np 1

    This assumes your data is in 4 columns (t,x,y,z) in file fort.8.
    The program, np, generates a PostScript file, plot.ps, which you
    can view by typing:

        ghostview plot.ps

    or you can print, by typing:

	lp plot.ps

    If you are on a Sun system other than ubunix or math, you will need to
    ftp the executable "np" and the instruction file "plot_descr_1.dat"
    to your directory on your machine.

(b) Locate all the equilibrium points of the system for general parameter
    values, and characterize all of them in the case of the parameter values
    used in (a).

(3) How would you approach the problem of locating all of the equilibrium
    points of the BZ model from the last homework? (Don't do it: just describe
    how you would, or why it's an impossible job, etc.)