Mechanical simulation tool based on impedance matrices

octopus is a simulation software specifically developed to calculate the response of a given mechanical system. The initial purpose of its development was to support the design and the commissioning of the superattenuator (SA), i.e., the vibration isolator designed to inhibit the transmission of the seismic noise at the level of the test mass of the Virgo gravitational waves detector. octopus analytically computes the transfer functions of a complex mechanical system using the impedance matrix formalism in the frequency domain and provides an advanced and versatile mechanical simulation tool. This methodology allows to analyze a large set of user-defined mechanical layouts. Within the context of advanced seismic isolation system design, the present software allows to accurately estimate the behavior of specific mechanical components in terms of performance and general requirements achievement, both in open loop and also when feedback control loops are implemented. In the present work, several topics will be addressed. First, the mathematical principles behind the impedance formalism will be introduced, focusing on the modeling of basic elements, which constitute the principal blocks used to develop and build complex mechanical models. Then, as case studies, two examples of mechanical systems models will be presented: the computation of the thermal noise of a body suspended by an elastic beam and the complete model of a superattenuator. To validate the accuracy of the simulation tool, comparisons with experimental measurements will be given in both cases.