  In this paper, we consider minimizing the action functional as a method for
numerically discovering periodic solutions to the $n$-body problem. With this
method, we can find a large number of choreographies and other more general
solutions. We show that most of the solutions found, including all but one of
the choreographies, are unstable. It appears to be much easier to find unstable
solutions to the $n$-body problem than stable ones. Simpler solutions are more
likely to be stable than exotic ones.
