  Adequate vibration isolation is of great importance for the design of any
sensitive experiment measuring mechanical motions. The so-called multistage or
multipole mechanical low pass filter is a common artifact used for the
construction of highly effective vibration isolation. However, the problem with
it is the vertical clearance needed inside the vacuum chambers for the
construction of numerous, long pendulum stages necessary for effective
horizontal vibration isolation. The purpose of this work is to introduce a new
concept, called the multi-nested pendula concept, which solves this problem.
The attenuation performance of an ideal multistage nested pendula filter is
better than that of an ideal multistage common equal pendula filter by a factor
of N^{N}, where N is the number of stages used, making this idea of a
multi-nested pendula a very interesting one. The initial results (of stability
and system resonances) measured for a prototype reinforce the viability of the
practical implementation of such idea. A detailed study for the realization of
a cryogenic and fully operational version to be used in LIGO is going to be
done in a future study.
