Mathematica Models of Pendulums
Before you can use any of the models on this page you need to install the pendulum modelling toolkit. See the toolkit page for download and installation instructions.
Compatibility Warning:
Several toolkit packages and all models had issues with Mathematica v6.0. (There were no additional problems with v7.0.) In particular the issue with the StatusWindow package was crippling: Mathematica would lock up. Don't even bother trying v6 or later until you've installed the 6/14/07 toolkit updates on the toolkit page. (The updates are recommended even if you're not going to be using v6 anytime soon - everything is backward compatible to v4.x.) With the toolkit updated you should be able to muddle through with the existing models under v6 or v7 except that the plotting of 3D modeshapes won't work. Updated versions of the models will be released by stages. Check back here for status. Updated models will be flagged with a marker: Mathematica v6.0 OK. Unfortunately it will be a slow process because the changes to the 3D graphics facilities are extensive enough that an entire new version of the eigenplot[] routine needs to be written for each model definition. Feel free to request priority treatment for a particular model. Models updated so far:
Quad Pendulum (Xtra-Lite Lateral)
Quad Pendulum (Xtra-Lite)
Quad Pendulum (Xtra-Lite Lateral Five-Bead Violin)
Triple Pendulum (Xtra-Lite)
Triple Pendulum (Xtra-Lite Five-Bead Violin)
Quad Models
A large number of variations on the basic quad model have been developed for different purposes. They all reflect the conceptual design of the test-mass suspension for Advanced LIGO, with 4 masses, 6 blade springs and 14 wires.
Quad Pendulum (Xtra-Lite Lateral) UPDATED 6/16/07 RECOMMENDED for AdvLIGO
Same as the xtra-lite quad pendulum but with lateral compliance of the blade tips. [Download] Mathematica 6 OK
Quad Pendulum (Xtra-Lite Lateral with 5-bead violin modes)
NEW 6/18/07
RECOMMENDED IF VIOLIN MODES ARE IMPORTANT - SUPERSEDES NON-LATERAL VERSION
Same as the xtra-lite lateral quad pendulum but with 5 beads in each of the fibres (lowest stage wires) to approximate the distributed mass and allow violin modes. [Download] Mathematica 6 OK
Quad Pendulum (Original)
The original version. The modeling of the blade springs is rather too fussy leading to large matrices and poor time domain simulation performance. [Download]
Quad Pendulum (Lite)
Same as the original quad pendulum but with less fussy modelling of the blade springs. The five non-working degrees of freedom of each spring tip relative to its base are eliminated with a geometrical constraint rather than being immobilized by stiff springs. This drastically reduces the size of the matrices (30x30 instead of 60x60) and eliminates many high frequency eigenmodes, making time-domain simulation more efficient. [Download]
Quad Pendulum (Xtra-Lite)
Same as the lite quad pendulum but even more minimalistic modelling of the blade springs. The mass element representing the tip has been eliminated, leaving only the 24 DOFs of the pendulum masses. [Download]
Quad Pendulum (Xtra-Lite Pitch/Lateral)
Same as the xtra-lite quad pendulum but with pitch and lateral (y) DOFs compliance the blade tips. The pitch effect is very small, so this is overkill for most purposes.) [Download]
Quad Pendulum (Xtra-Lite Version 2D)
Same as the xtra-lite quad pendulum but with all y, yaw and roll DOFs suppressed. [Download]
Quad Pendulum (Xtra-Lite with 5-bead Violin Modes)
Formerly recommended, but superceded by the Xtra-Lite Lateral with 5-bead Violin Modes. Same as the xtra-lite lateral quad pendulum but with 5 beads in each of the fibres (lowest stage wires) to approximate the distributed mass and allow violin modes. [Download] Mathematica 6 OK
GEO-style, 6-Blade Triple Models
A number of variations on the basic triple model have been developed for different purposes. They all reflect the conceptual design of GEO triple (or the mode-cleaner for Advanced LIGO), with 3 masses, 6 blade springs and 10 wires.
Triple Pendulum
This model reflects the design developed for GEO, with 3 masses, 6 blade springs and 10 wires. [Download]
Triple Pendulum (Lite Version)
Same as the full triple pendulum but with less fussy modelling of the blade springs. The five non-working degrees of freedom of each spring tip relative to its base are eliminated with a geometrical constraint rather than being immobilized by stiff springs. This drastically reduces the size of the matrices (24x24 instead of 54x54) and eliminates many high frequency eigenmodes, making time-domain simulation more efficient. [Download]
Triple Pendulum (Xtra-Lite) Updated 6/20/07 RECOMMENDED - Mathematica 6 OK
Same as the lite triple pendulum but even more minimalistic modelling of the blade springs. The mass element representing the tip has been eliminated, leaving only the 18 DOFs of the pendulum masses. [Download]
Triple Pendulum (Xtra-Lite Five-Bead Violin) 6/21/07 RECOMMENDED - Mathematica 6 OK
Same as the xtra-lite triple pendulum with five mass beads in the bottom wires/fibres to approximate violin modes. [Download]
Triple Pendulum with Blade Lateral Compliance (Xtra-Lite Version)
Same as the xtra-lite triple pendulum with blade springs that can flex laterally as well as in vertical. [Download]
AdvLIGO-style, 4-Blade Triple Models
Double-Blade Triple Pendulum Xtra-Lite
Same as the xtra-lite GEO-style triple pendulum but with only two blades rather than four at the top mass. [Download]
Double-Blade Triple Pendulum Xtra-Lite With Blade Lateral Compliance
Same as the xtra-lite double-blade triple pendulum but with blade lateral compliance. [Download]
LIGO-I
Two-Wire Simple Pendulum
A two-wire, LIGO-I-style simple pendulum. [Download]
Two-Wire Simple Pendulum 2D
A two-wire, LIGO-I-style simple pendulum, with y, yaw and roll suppressed. [Download]
Toy Models
One-Wire Simple Pendulum
This is a toy model of a one-wire simple pendulum for validation of the provisions for calculating the effect of the wire bending and the resulting thermal noise. [Download]
One-Wire Simple Pendulum 2D
As for the one-wire simple pendulum, but with y, yaw and roll DOFs suppressed for convenience in investigating the wire flexure correction. [Download]
One-Wire Super-Simple Pendulum 2D
A 2D one-wire pendulum with not only y, yaw and roll suppressed but with the bob reduced to a point mass with no MOI or pitch DOF. [Download]
Two-Wire Simple Pendulum
See above under LIGO-I
Four-Wire Simple Pendulum 2D
As for the four-wire simple pendulum, but with y, yaw and roll DOFs suppressed for convenience in investigating the wire flexure correction. [Download]
Four-Wire Simple Pendulum With Five-Bead Violin Modes
As for the four-wire simple pendulum above, with five beads in each fibre to approximate the distributed mass and allow violin modes. [Download]
Four-Wire Two-Mass Pendulum 2D
A pendulum with a lower mass supported by four wires from an upper mass hinged about a transverse axis (similar to the bottom two masses of a quad). The y, roll and yaw DOFs have been suppressed. (There is no full/3D version of this model.) [Download]
Four-Wire Two-Mass Pendulum 2D Lite
As for the four-wire two-mass pendulum, but with the x DOF of the lower mass suppressed as well. [Download]