Matlab code

The code:

Explaination for line 7 – 9:
The position vector, r, can be expressed as:

where

We see that

For

, and thus,

we have:

.


y=

=

Substitute
equation gives:

and

into the

This is a function of y with respect to a single variable, x.
Line 7:

(needs teacher’s help)

Line 8 and 9:
Since MATLAB does not include any syntax for ± operation, we need to split the equation into 2 separated sub-function
y1 (plus sign) and y2 (minus sign). Then we can plot the trajectory later using each of the y function respectively.

Some examples to test the above code:
Case 1:
a)

:


b)


Case 2:
a)

b)


c) In a special case where x0 = y0


Case 3 (general cases):

+ If

If