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<title>A Practical Guide to Tensegrity Design:
6.2.5&nbsp;Dome Step 5:  Compute the dome</title>
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<p class="link">
A Practical Guide to Tensegrity Design<br/>
<a href="index.html#chap6_2_5">Table of Contents</a><br/>
6.2.4&nbsp;<a href="chap6_2_4.xml">Dome Step 4:  Add guys</a>
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6.2.5&nbsp;Dome Step 5:  Compute the dome
</p>

<p>
As usual, the structure is computed by minimizing a weighted combination
of the interlayer and binding tendons subject
to constraints on the struts and convergence tendons.
The big difference is the base points are kept fixed.  In addition
to providing the benefits mentioned previously, fixing
these points also makes the structure mathematically determinate.
</p>

<!-- Ref:  Notes 1/15/93, tenseg/v06oct/laminar/trunc3/stage1_2004.rc -->

<p>
Two initial iterations are done using the penalty formulation
<math xmlns="&mathml;"><mfenced>
<mrow><mover><mi>&mu;</mi><mo>&OverBar;</mo></mover><mo>=</mo>
<msup><mn>10</mn><mn>5</mn></msup></mrow></mfenced></math>
in conjunction
with Fletcher-Reeves to bring the initial points into approximate
conformance with the constraints.  The source of the initial non-conformity
with the constraints is the adjustment of the base points that is
done in <a href="chap6_2_3.xml">Step&nbsp;3</a>.
After this three iterations are
done with the exact formulation in conjunction with Fletcher-Reeves to
bring the values to convergence.  The derivatives of
the objective function with respect to the independent
coordinate values are all less than
<math xmlns="&mathml;"><msup><mn>10</mn><mn>-5</mn></msup></math>.
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<p class="link">
<a href="index.html#chap6_2_5">Table of Contents</a><br/>
6.2.6&nbsp;<a href="chap6_2_6.xml">Dome Step 6:
Make adjustments to fix problems</a>
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