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   <text:h text:style-name="Heading_20_1" text:outline-level="1">Nondimensionalize the equations of motion</text:h>
   <text:p text:style-name="Standard"><draw:frame draw:style-name="fr1" draw:name="Object12" text:anchor-type="as-char" svg:width="0.7618in" svg:height="0.4201in" draw:z-index="0"><draw:object>
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            <mi>g</mi>
            <mi>c</mi>
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         <mi>m</mi>
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{g_c}
m
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   <text:p text:style-name="Standard">Define characteristic mass,<draw:frame draw:style-name="fr1" draw:name="Object1" text:anchor-type="as-char" svg:width="0.2563in" svg:height="0.2102in" draw:z-index="1"><draw:object>
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       AAAAAAAApwEAAAAAAAAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIAAAABAIcA
       AQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAGoAAAByAQAAAQBtMQEAAAAA//8BAG0A
       jAABAAAAAACLAAEAAgAAAB8AigABADsAAAADADUAAAAJAFRob3JuZGFsZQAAAAAAAP0AAAAA
       AAAAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCHAAEABQAAAP////8A
       hgABAAQAAAAAAAAAcgACABcAAACnAQAA3AEAAAEAY3IAAAAAAP//AQBjAIwAAQAAAAAAlQAB
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    </draw:frame>, equal the maximum mass.</text:p>
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         <mi>L</mi>
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       AAAAAAAApwEAAAAAAAAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIAAAABAIcA
       AQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAIQAAAByAQAAAQBM5QAAAAAA//8BAEwA
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       hgABAAQAAAAAAAAAcgACABcAAAByAQAA3AEAAAEAY3IAAAAAAP//AQBjAIwAAQAAAAAAlQAB
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    </draw:frame>, equal the rms of all distances of markers from the cg..</text:p>
   <text:p text:style-name="Standard">Define characteristic time,<draw:frame draw:style-name="fr1" draw:name="Object3" text:anchor-type="as-char" svg:width="0.1866in" svg:height="0.2102in" draw:z-index="3"><draw:object>
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       AAAAAAAApwEAAAAAAAAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIAAAABAIcA
       AQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAGoAAAByAQAAAQB0cgAAAAAA//8BAHQA
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   <text:p text:style-name="Standard">Then the characteristic force,<draw:frame draw:style-name="fr1" draw:name="Object4" text:anchor-type="as-char" svg:width="0.2535in" svg:height="0.2102in" draw:z-index="4"><draw:object>
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    </draw:frame>, is defined as follows.</text:p>
   <text:p text:style-name="Standard"><draw:frame draw:style-name="fr1" draw:name="Object5" text:anchor-type="as-char" svg:width="0.8957in" svg:height="0.4638in" draw:z-index="5"><draw:object>
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{F_c}
=
{m}
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{m_c}
{{bold nitalic a}t^2_c}
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{L_c}</annotation>
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   <text:h text:style-name="Heading_20_1" text:outline-level="1">CAD user units</text:h>
   <text:p text:style-name="Standard">The CAD user defines units for time, mass, aJ, length, angle, velocity, omega, acceleration, alpha, force, torque. Internally, GEO stores everything in SI units. We want to store all user inputs as formulas in text form so that user inputs are repeatable and not mutated by numerical errors. We also want to store past formulas for possible reuse or parametric study. </text:p>
   <text:p text:style-name="Standard"/>
   <text:p text:style-name="Standard">What happens when the CAD user decided to change his units? </text:p>
   <text:p text:style-name="Standard">We modify the formulas symbolically by the conversion factors and save the previous formulas.</text:p>
   <text:p text:style-name="Standard"/>
   <text:p text:style-name="Standard">What must a formula store?</text:p>
   <text:p text:style-name="Standard">A formula must store the text of the formula, its own unit, units for the functions and variables in the formula, past formulas and its container.</text:p>
   <text:p text:style-name="Standard"/>
  </office:text>
 </office:body>
</office:document>