Next: About this document ...
ASTR615 Fall 2015 Problem Set #3
Due Oct 21, 2015
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
 |
(1) |
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.
Next: About this document ...
Massimo Ricotti
2015-10-06