Reproduce the results on page 41
using a matlab program to solve
equations 1.6 on page 40.
A link to the original paper can be found here.
Pt I. Show (numerically)
that given two bodies (mass m1 and m2)
there is a stable orbit where both bodies revolve about the
center of mass. (Assume the orbits lie in a plane).
Pt II. Assume that m1=m2, and add a third body m3 (much much smaller than m1=m2) and show that there are conditions for m3 which result in a complex, even chaotic, orbit.
[Use MATLAB's built in ode solver, ode45]. See derivation of 2-body equations
| Using the 1-D data
sets found here, use (or modify)
Note, you must be careful to make good use of all the data, since some of the data sets may be contaminated with "white noise."
MATLAB (Extra Credit)
1. Download the file "Mandel121" from Matlab Central
Mandel121 Files). Click on the "Download now" and download
the file mandel15nov08.zip to a directory on your computer.
2. Unzip the file on your pc with "Winzip" or equivalent. Alternately, transfer the file to your calclab1.math.tamu.edu account (with WinSCP or equivalent) and unzip with the command "unzip mandel15nov08.zip". It will create a directory called "mandel08nov08".
3. Run the program "mandel125" (make sure you navigate to the proper directory before running it). In the directory there is a file called "dummy2.m". The file contains the function that is iterated (line 47).
4. Change the function, for example to,
z(h_z)=z(h_z).^2+0.02*z(h_z).^3+c(h_z);5. Your assignment is to classify the different kinds of regions within the default Mandelbrot set (z(h_z)=z(h_z).^2+c(h_z)) and the change the function to see how the geometry changes.
In your write up, be sure to include lots of graphics from the mandel125 program!