Toolkit

The toolkit is a set of Mathematica packages which provide support for the following:

• rigid body masses with x, y, z, yaw, pitch and roll DOFs
• wires or ribbons, without distributed mass (no true violin modes) but with a detailed elasticity model including longitudinal, torsional, and bending near the attachment points
• spring elements with a 6*6 stiffness matrix and a 6 component vector of preload forces/torques
• optional massless connecting elements between elastic elements
• arbitrary frequency-dependent damping on all sources of elasticity
• dissipation dilution
• fully symbolic expressions for the potential and kinetic energy
• numerical solutions for the minimum of the potential and the eigenvalues and eigenvectors
• ::usage tags defined for all symbols (for use with the Mathematica help operator "?")
• utility functions to plot mode shapes, transfer functions and thermal noise
• automatic saving of results of time-consuming calculations for easy reloading later
• a default parameter set which is easily overridable to reflect design variations
• export of state-space matrices to Matlab and/or E2E

See the Toolkit page for download and installation instructions.

Mathematica Models

Using this toolkit, I've developed models of a generic GEO-style triple pendulum, and a generic quad pendulum as proposed for Advanced LIGO, as well as many toy models. See the Models page for download and installation instructions.

Matlab Versions of Models

• A set of numerical state-space matrices is exported for a specific model and set of numerical parameters. The toolkit has functions for this.
• The usual Mathematica calculation is intercepted just before numerical values are inserted, and symbolic state-space matrices are exported. Numerical parameters are applied later in the Matlab. This takes some tricky custom code, but has been done for the most important models.

In both cases, a simple Matlab program reads in the exported matrices and loads them into a Simulink model. The Matlab wrapper is packaged with the matrices.

Links to the Matlab versions can be found both on the pages of the equivalent Mathematica models and on the Matlab page.

E2E Versions of Models

Results from selected models have been exported in text format suitable for use with the E2E/Alfi modeling package. An output file has four lines to be pasted into the A, B, C and D fields of an "SSPend" block. Links to the E2E versions can be found both on the pages of the equivalent Mathematica models and on the E2E page.