Topics for this problem set include round-off error and linear algebra.

- As an example of an unstable algorithm, consider integer
powers of the ``Golden Mean''
. It can be
shown that
, i.e. successively
higher powers of can be computed from a single subtraction
rather than a more expensive multiply. Write a single-precision
program to compute a table consisting of the columns ,
computed from the recursion relation, and computed directly
(i.e.
), for ranging from 1 to 20. Is
the round-off error random? What happens in double precision?
- Write a program to compute the instantaneous spin period of a
rigid body made up of identical, discrete, point particles. Use the
fact that the angular momentum is

where is the mass of particle , and are its position and velocity vectors with respect to the centre of mass, is the spin vector, and is the inertia tensor

where is the unit matrix.*[For continuous bodies the summations are replaced by volume integrations and the particle masses become a mass density. In the present case the 's can be omitted entirely since the particles are identical.]*Write a program to solve Eq. () for (feel free to use the routines in*Numerical Recipes).*The spin period is then .- Test your code by reading the data file
http://www.astro.umd.edu/~ricotti/NEWWEB/teaching/ASTR415/ps2.dat

which is in the format (i.e. 6 values to a line separated by white space). The units are mks (SI). What is the spin period in hours? - Make a graphical representation of the body using your
favorite graphing package. If you use 2-D projections, be sure to
include enough viewing angles to get a complete picture.

- Test your code by reading the data file