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18 changes: 10 additions & 8 deletions contributing/contributing.html
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Expand Up @@ -561,6 +561,7 @@ <h2>Notebook Creation<a class="headerlink" href="#notebook-creation" title="Perm
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+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| of &#39;&lt;variable&gt;&#39; | wrt &#39;&lt;variable&gt;&#39; | calc mag. | check mag. | a(cal-chk) | r(cal-chk) | error desc |
+=================+==================+=============+=============+=============+=============+============+
| &#39;check&#39; | &#39;theta&#39; | 9.8147e+02 | 9.8147e+02 | 2.2749e-13 | 2.3179e-16 | |
| &#39;check&#39; | &#39;theta&#39; | 4.3887e+01 | 4.3887e+01 | 1.5993e-14 | 3.6442e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;check&#39; | &#39;v&#39; | 1.2709e+01 | 1.2709e+01 | 1.1322e-15 | 8.9090e-17 | |
| &#39;check&#39; | &#39;v&#39; | 3.4590e+00 | 3.4590e+00 | 4.9651e-16 | 1.4354e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;theta&#39; | 1.4431e+01 | 1.4431e+01 | 2.8109e-15 | 1.9477e-16 | |
| &#39;vdot&#39; | &#39;theta&#39; | 1.6571e+01 | 1.6571e+01 | 3.6621e-15 | 2.2100e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;v&#39; | 0.0000e+00 | 0.0000e+00 | 0.0000e+00 | nan | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;theta&#39; | 8.5390e+00 | 8.5390e+00 | 2.8262e-15 | 3.3097e-16 | |
| &#39;xdot&#39; | &#39;theta&#39; | 1.2690e+01 | 1.2690e+01 | 1.3323e-15 | 1.0499e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;v&#39; | 1.4716e+00 | 1.4716e+00 | 2.0015e-16 | 1.3601e-16 | |
| &#39;xdot&#39; | &#39;v&#39; | 1.6897e+00 | 1.6897e+00 | 3.5108e-16 | 2.0778e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;theta&#39; | 1.1471e+01 | 1.1471e+01 | 8.9164e-16 | 7.7733e-17 | |
| &#39;ydot&#39; | &#39;theta&#39; | 1.4053e+01 | 1.4053e+01 | 1.9860e-15 | 1.4133e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;v&#39; | 1.6836e+00 | 1.6836e+00 | 2.4980e-16 | 1.4837e-16 | |
| &#39;ydot&#39; | &#39;v&#39; | 1.4645e+00 | 1.4645e+00 | 3.1891e-16 | 2.1775e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+

##################################################################
Expand All @@ -752,7 +753,7 @@ <h2>Notebook Creation<a class="headerlink" href="#notebook-creation" title="Perm
+-----------------+------------------+-------------+-------------+-------------+-------------+
| of &#39;&lt;variable&gt;&#39; | wrt &#39;&lt;variable&gt;&#39; | calc mag. | check mag. | a(cal-chk) | r(cal-chk) |
+=================+==================+=============+=============+=============+=============+
| &#39;xdot&#39; | &#39;theta&#39; | 8.5390e+00 | 8.5390e+00 | 2.8262e-15 | 3.3097e-16 |
| &#39;check&#39; | &#39;theta&#39; | 4.3887e+01 | 4.3887e+01 | 1.5993e-14 | 3.6442e-16 |
+-----------------+------------------+-------------+-------------+-------------+-------------+
</pre></div>
</div>
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62 changes: 31 additions & 31 deletions examples/balanced_field/balanced_field.html
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Expand Up @@ -576,13 +576,13 @@ <h2>The ODE System<a class="headerlink" href="#the-ode-system" title="Permalink
<h3>The Aerodynamic Model<a class="headerlink" href="#the-aerodynamic-model" title="Permalink to this heading">#</a></h3>
<p>Both sets of equations of motion have common aerodynamic models.</p>
<p>First, the lift coefficient is computed using a model which assumes linearity in lift wrt the angle of attack.</p>
<div class="amsmath math notranslate nohighlight" id="equation-eb13c583-d2ff-40f0-b2bd-a104fc6be1ad">
<span class="eqno">(21)<a class="headerlink" href="#equation-eb13c583-d2ff-40f0-b2bd-a104fc6be1ad" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-be37a592-925a-4729-adf1-63ac3e125323">
<span class="eqno">(21)<a class="headerlink" href="#equation-be37a592-925a-4729-adf1-63ac3e125323" title="Permalink to this equation">#</a></span>\[\begin{align}
C_L &amp;= C_{L0} + \frac{\alpha}{\alpha_{max}} \left(C_{L-max} - C_{L0}\right)
\end{align}\]</div>
<p>Next, the drag-due-to-lift factor is computed (Equations 12.48 and 12.61 in Raymer[&#64;raymer2012aircraft]).</p>
<div class="amsmath math notranslate nohighlight" id="equation-e3d3fb68-6c7e-4bb2-b159-eee7de9f8f96">
<span class="eqno">(22)<a class="headerlink" href="#equation-e3d3fb68-6c7e-4bb2-b159-eee7de9f8f96" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-854862a6-40fd-48fe-b0da-420f9135bb92">
<span class="eqno">(22)<a class="headerlink" href="#equation-854862a6-40fd-48fe-b0da-420f9135bb92" title="Permalink to this equation">#</a></span>\[\begin{align}
K_{nom} &amp;= \frac{1}{ \pi AR e} \\
b &amp;= \frac{span}{2} \\
K &amp;= 33 K_{nom} \frac{ \left(\frac{h + h_w}{b} \right) ^{\frac{3}{2}}}{1.0 + 33 \left( \frac{h + h_w}{b}\right) ^{\frac{3}{2}}}
Expand All @@ -591,8 +591,8 @@ <h3>The Aerodynamic Model<a class="headerlink" href="#the-aerodynamic-model" tit
This causes this problem to be difficult to solve using a shooting method.
If the optimizer proposes a combination of initial states and a control history that results in altitude dropping significantly below zero, the propagation will fail.</p>
<p>Finally, the lift and drag are computed after computing the dynamic pressure.</p>
<div class="amsmath math notranslate nohighlight" id="equation-d923400c-f294-4b54-a143-815eb3c84770">
<span class="eqno">(23)<a class="headerlink" href="#equation-d923400c-f294-4b54-a143-815eb3c84770" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-fd3da30e-1b75-4fe2-91a8-760c9c4fc21e">
<span class="eqno">(23)<a class="headerlink" href="#equation-fd3da30e-1b75-4fe2-91a8-760c9c4fc21e" title="Permalink to this equation">#</a></span>\[\begin{align}
q &amp;= 0.5 \rho v^2 \\
L &amp;= q S C_L \\
D &amp;= q S \left( C_{D0} + K C_{L}^2 \right)
Expand All @@ -603,17 +603,17 @@ <h3>Stall Speed<a class="headerlink" href="#stall-speed" title="Permalink to thi
<p>This model relies on the ratio of the current true airspeed to stall speed (<span class="math notranslate nohighlight">\(\frac{v}{v_{stall}}\)</span>).
This constraint is used to trigger the beginning of rotation and is used as a boundary constraint at the end of the initial climb.
Stall speed is given by Equation 5.6 in Raymer[&#64;raymer2012aircraft].</p>
<div class="amsmath math notranslate nohighlight" id="equation-2e71e0bc-15ca-4303-b515-772f138adaa7">
<span class="eqno">(24)<a class="headerlink" href="#equation-2e71e0bc-15ca-4303-b515-772f138adaa7" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-0d239304-2df7-4a8d-990a-f582990aecd5">
<span class="eqno">(24)<a class="headerlink" href="#equation-0d239304-2df7-4a8d-990a-f582990aecd5" title="Permalink to this equation">#</a></span>\[\begin{align}
W &amp;= m g \\
v_{stall} &amp;= \sqrt{\frac{2 * W}{\rho S C_{L-max}}}
\end{align}\]</div>
</section>
<section id="runway-equations-of-motion">
<h3>Runway Equations of Motion<a class="headerlink" href="#runway-equations-of-motion" title="Permalink to this heading">#</a></h3>
<p>The runway equations of motion are used to integrate range and speed as the vehicle rolls along the runway.</p>
<div class="amsmath math notranslate nohighlight" id="equation-b9acdf38-8b25-493c-835f-22a6eb8abb3e">
<span class="eqno">(25)<a class="headerlink" href="#equation-b9acdf38-8b25-493c-835f-22a6eb8abb3e" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-1fd45f2b-2bc9-4265-985c-18fc4488552a">
<span class="eqno">(25)<a class="headerlink" href="#equation-1fd45f2b-2bc9-4265-985c-18fc4488552a" title="Permalink to this equation">#</a></span>\[\begin{align}
F_r &amp;= mg - L \cos \alpha - T \sin \alpha \\
\dot{v} &amp;= \frac{T \cos \alpha - D - F_r \mu_r}{m} \\
\dot{r} &amp;= v
Expand All @@ -640,8 +640,8 @@ <h3>Runway Equations of Motion<a class="headerlink" href="#runway-equations-of-m
<section id="flight-equations-of-motion">
<h3>Flight Equations of Motion<a class="headerlink" href="#flight-equations-of-motion" title="Permalink to this heading">#</a></h3>
<p>The flight equations of motion include two additional state variables: the flight-path angle (<span class="math notranslate nohighlight">\(\gamma\)</span>) and altitude (<span class="math notranslate nohighlight">\(h\)</span>).</p>
<div class="amsmath math notranslate nohighlight" id="equation-f08a6c7e-ad29-4026-9cf0-b9bc251239b9">
<span class="eqno">(26)<a class="headerlink" href="#equation-f08a6c7e-ad29-4026-9cf0-b9bc251239b9" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-511f8f40-92a9-42dd-8c2f-6f7310dbe45d">
<span class="eqno">(26)<a class="headerlink" href="#equation-511f8f40-92a9-42dd-8c2f-6f7310dbe45d" title="Permalink to this equation">#</a></span>\[\begin{align}
\dot{v} &amp;= \frac{T}{m} \cos \alpha - \frac{D}{m} - g \sin \gamma \\
\dot{\gamma} &amp;= \frac{T}{m v} \sin \alpha + \frac{L}{m v} - \frac{g \cos \gamma}{v} \\
\dot{h} &amp;= v \sin \gamma \\
Expand Down Expand Up @@ -1165,7 +1165,7 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;dymos.phase.phase.Phase at 0x7f01bcf53af0&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;dymos.phase.phase.Phase at 0x7f75608036d0&gt;
</pre></div>
</div>
</div>
Expand Down Expand Up @@ -1309,8 +1309,9 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
[final] 5.0000e+00 == gam [deg]
[final] 1.2500e+00 &lt;= v_over_v_stall [None]
[path] 0.0000e+00 &lt;= gam &lt;= 5.0000e+00 [deg]

INFO: checking out_of_order
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>INFO: checking out_of_order
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>INFO:check_config:checking out_of_order
Expand Down Expand Up @@ -1426,20 +1427,19 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.3% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.022397 sec.
Time to compute coloring: 0.015122 sec.
Time to compute sparsity: 0.025429 sec.
Time to compute coloring: 0.018797 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Coloring for &#39;traj.phases.rto.rhs_all&#39; (class BalancedFieldODEComp)

Coloring for &#39;traj.phases.rto.rhs_all&#39; (class BalancedFieldODEComp)

Jacobian shape: (132, 60) ( 9.79% nonzero)
FWD solves: 16 REV solves: 0
Total colors vs. total size: 16 vs 60 (73.3% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.020197 sec.
Time to compute coloring: 0.014614 sec.
Time to compute sparsity: 0.024386 sec.
Time to compute coloring: 0.017943 sec.
Memory to compute coloring: 0.000000 MB.

Coloring for &#39;traj.phases.v1_to_vr.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1449,8 +1449,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.3% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.019348 sec.
Time to compute coloring: 0.014845 sec.
Time to compute sparsity: 0.024096 sec.
Time to compute coloring: 0.018141 sec.
Memory to compute coloring: 0.000000 MB.

Coloring for &#39;traj.phases.rotate.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1460,8 +1460,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.3% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.019450 sec.
Time to compute coloring: 0.014961 sec.
Time to compute sparsity: 0.025099 sec.
Time to compute coloring: 0.018130 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
Expand All @@ -1472,12 +1472,12 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 111 (85.6% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.040187 sec.
Time to compute coloring: 0.029838 sec.
Time to compute sparsity: 0.052630 sec.
Time to compute coloring: 0.036409 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Full total jacobian was computed 3 times, taking 1.429048 seconds.
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Full total jacobian was computed 3 times, taking 1.872126 seconds.
Total jacobian shape: (178, 166)


Expand All @@ -1486,8 +1486,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 12 vs 166 (92.8% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 1.429048 sec.
Time to compute coloring: 0.102081 sec.
Time to compute sparsity: 1.872126 sec.
Time to compute coloring: 0.128597 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
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