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<H3><A NAME="SECTION00625400000000000000">
Periodic Variables</A>
</H3>
We must tell DsTool whether our phase space contains any periodic variables. The
coding of this information is accomplished through two C-language constants:
EUCLIDEAN or PERIODIC. If there are no periodic variables, then
the phase space is EUCLIDEAN; if there is at least one periodic variable, the
phase space is classified as PERIODIC. For PERIODIC phase spaces, we must
also inform DsTool as to which variables are periodic and what interval to use as
a fundamental domain.
<P>
For our example, since the equations of motion are invariant under the transformation
<!-- MATH: $\phi \to \phi + 2 n \pi$ -->
78#78
for any integer <I>n</I>, we may consider 64#64
to be a
periodic variable with period 82#82.
We may choose <EM>any</EM> interval of length
82#82
as a fundamental domain for the variable 64#64.
Common choices are
the intervals
<!-- MATH: $[-\pi, \pi]$ -->
85#85
and
<!-- MATH: $[0, 2 \pi]$ -->
80#80.
We make the latter choice.
To pass this information into DsTool, we edit yet a few more lines in bball_init():
<PRE>
int manifold_type=PERIODIC; /* EUCLIDEAN or PERIODIC */
static int periodic_varb[]={TRUE, FALSE}; /* if PERIODIC, which varbs periodic? */
static double period_start[]={0.,0.}; /*if PERIODIC, begin fundamental domain */
static double period_end[]={TWOPI, 1.}; /*if PERIODIC, end of fundamental domain*/
</PRE>
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We remark on the variables period_start and
period_end. If the <I>j</I>th coordinate is not periodic (, the
value of periodic_varb[<I>j</I>] is FALSE) then it does not
matter what period_start[<I>j</I>] and period_end[<I>j</I>] are because
the entries are ignored by DsTool. Similarly, if the variable
manifold_type is EUCLIDEAN, then it doesn't matter what
values are given for the entries of periodic_varb. It is
always safe, of course, to set each entry of periodic_varb to
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<ADDRESS>
<I>John Lapeyre</I>
<BR><I>1998-09-04</I>
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