Tethys' Lagrangian Points and Telesto/Calypso

Hi,

On Wikipedia, it is said that several moons have companion moons in their
Lagrangian points, such as Tethys
http://en.wikipedia.org/wiki/Natural_satellite). After looking the data on
Tethys, such moons are Telesto and Calypso, residing in L4 and L5 of
Tethys. What I expect is the three moons will have the same semi-major
axis, orbital period and inclination around Saturn and Saturn's Equatorial
plane, respectively. While the semi-major axis and orbital period is
confirmed, the inclinations are different, with

Tethys : 1.12
Telesto: 1.19
Calypso: 1.56

I'm under the impression that the Lagrangian points are all on the plane in
which the satellite orbits the main body. If that is true, considering
Saturn is the main body, and Tethys is the satellite, then why Telesto and
Calypso have different inclinations?

If the lagrangian points doesn't have to be on such plane, then,
considering the plane on which the satellite is orbiting the main body as
the XZ plane in Cartesian system, what are the constraints of the points'
location on the Y axis?

TIA
.

Relevant Pages

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