The time reversal symmetry across the *y =* 0 plane can be
exploited to find certain periodic orbits. If a trajectory pierces
the *y =* 0 plane such that it is perpendicular to the plane we
know that it is "attached" to its symmetric counterpart. If the
trajectory again intersects the *y = *0 plane perpendicularly
then it and its symmetric partner form a loop; a periodic orbit.

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