<s>
Weak	B-Algorithm
stability	I-Algorithm
boundary	I-Algorithm
(	O
WSB	O
)	O
,	O
including	O
Low-energy	O
transfer	O
,	O
is	O
a	O
concept	O
introduced	O
by	O
Edward	O
Belbruno	O
in	O
1987	O
.	O
</s>
<s>
Weak	B-Algorithm
stability	I-Algorithm
boundary	I-Algorithm
is	O
defined	O
for	O
the	O
three-body	O
problem	O
.	O
</s>
<s>
The	O
weak	B-Algorithm
stability	I-Algorithm
boundary	I-Algorithm
defines	O
a	O
region	O
about	O
P2	O
where	O
P	O
is	O
temporarily	O
captured	O
.	O
</s>
<s>
The	O
set	O
of	O
all	O
transition	O
points	O
about	O
the	O
Moon	O
comprises	O
the	O
weak	B-Algorithm
stability	I-Algorithm
boundary	I-Algorithm
,	O
W	O
.	O
The	O
motion	O
of	O
P	O
is	O
sensitive	O
or	O
chaotic	O
as	O
it	O
moves	O
about	O
the	O
Moon	O
within	O
W	O
.	O
A	O
mathematical	O
proof	O
that	O
the	O
motion	O
within	O
W	O
is	O
chaotic	O
was	O
given	O
in	O
2004	O
.	O
</s>
<s>
The	O
weak	B-Algorithm
stability	I-Algorithm
boundary	I-Algorithm
was	O
originally	O
referred	O
to	O
as	O
the	O
fuzzy	O
boundary	O
.	O
</s>
<s>
It	O
defines	O
W	O
relative	O
to	O
n-cycles	O
,	O
where	O
n	O
=	O
1	O
,	O
2	O
,	O
3	O
,...,	O
yielding	O
boundaries	O
of	O
order	O
n	O
.	O
This	O
gives	O
a	O
much	O
more	O
complex	O
region	O
consisting	O
of	O
the	O
union	O
of	O
all	O
the	O
weak	B-Algorithm
stability	I-Algorithm
boundaries	I-Algorithm
of	O
order	O
n	O
.	O
This	O
definition	O
was	O
explored	O
further	O
in	O
2010	O
.	O
</s>
<s>
The	O
results	O
suggested	O
that	O
W	O
consists	O
,	O
in	O
part	O
,	O
of	O
the	O
hyperbolic	O
network	O
of	O
invariant	O
manifolds	O
associated	O
to	O
the	O
Lyapunov	O
orbits	O
about	O
the	O
L1	O
,	O
L2	O
Lagrange	B-Application
points	I-Application
near	O
P2	O
.	O
</s>
<s>
The	O
explicit	O
determination	O
of	O
the	O
set	O
W	O
about	O
P2	O
=	O
Jupiter	O
,	O
where	O
P1	O
is	O
the	O
Sun	O
,	O
is	O
described	O
in	O
"	O
Computation	O
of	O
Weak	B-Algorithm
Stability	I-Algorithm
Boundaries	I-Algorithm
:	O
Sun-Jupiter	O
Case	O
"	O
.	O
</s>
<s>
A	O
proof	O
of	O
the	O
existence	O
of	O
the	O
weak	B-Algorithm
stability	I-Algorithm
boundary	I-Algorithm
about	O
P1	O
was	O
given	O
in	O
2012	O
,	O
but	O
a	O
different	O
definition	O
is	O
used	O
.	O
</s>
<s>
The	O
chaos	O
of	O
the	O
motion	O
is	O
analytically	O
proven	O
in	O
"	O
Geometry	O
of	O
Weak	B-Algorithm
Stability	I-Algorithm
Boundaries	I-Algorithm
"	O
.	O
</s>
<s>
The	O
boundary	O
is	O
studied	O
in	O
"	O
Applicability	O
and	O
Dynamical	O
Characterization	O
of	O
the	O
Associated	O
Sets	O
of	O
the	O
Algorithmic	O
Weak	B-Algorithm
Stability	I-Algorithm
Boundary	I-Algorithm
in	O
the	O
Lunar	O
Sphere	O
of	O
Influence	O
"	O
.	O
</s>
<s>
There	O
are	O
a	O
number	O
of	O
important	O
applications	O
for	O
the	O
weak	B-Algorithm
stability	I-Algorithm
boundary	I-Algorithm
(	O
WSB	O
)	O
.	O
</s>
<s>
This	O
is	O
the	O
first	O
reference	O
for	O
ballistic	O
capture	O
for	O
spacecraft	O
and	O
definition	O
of	O
the	O
weak	B-Algorithm
stability	I-Algorithm
boundary	I-Algorithm
.	O
</s>
<s>
Other	O
missions	O
have	O
used	O
the	O
same	O
transfer	O
type	O
as	O
Hiten	O
,	O
that	O
include	O
Grail	B-Protocol
,	O
Capstone	O
,	O
Danuri	O
.	O
</s>
