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16 changes: 8 additions & 8 deletions contributing/contributing.html
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Expand Up @@ -729,21 +729,21 @@ <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) | error desc |
+=================+==================+=============+=============+=============+=============+============+
| &#39;check&#39; | &#39;theta&#39; | 3.2681e+01 | 3.2681e+01 | 3.9784e-15 | 1.2173e-16 | |
| &#39;check&#39; | &#39;theta&#39; | 9.4575e+02 | 9.4575e+02 | 3.5954e-13 | 3.8016e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;check&#39; | &#39;v&#39; | 3.9773e+00 | 3.9773e+00 | 3.1402e-16 | 7.8953e-17 | |
| &#39;check&#39; | &#39;v&#39; | 1.2151e+01 | 1.2151e+01 | 2.0830e-15 | 1.7143e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;theta&#39; | 1.5960e+01 | 1.5960e+01 | 3.7682e-15 | 2.3610e-16 | |
| &#39;vdot&#39; | &#39;theta&#39; | 1.3497e+01 | 1.3497e+01 | 2.6761e-15 | 1.9827e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;v&#39; | 0.0000e+00 | 0.0000e+00 | 0.0000e+00 | nan | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;theta&#39; | 7.6817e+00 | 7.6817e+00 | 9.4216e-16 | 1.2265e-16 | |
| &#39;xdot&#39; | &#39;theta&#39; | 1.2777e+01 | 1.2777e+01 | 5.5943e-17 | 4.3784e-18 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;v&#39; | 1.6275e+00 | 1.6275e+00 | 3.7649e-16 | 2.3134e-16 | |
| &#39;xdot&#39; | &#39;v&#39; | 1.3763e+00 | 1.3763e+00 | 2.7371e-16 | 1.9888e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;theta&#39; | 8.4420e+00 | 8.4420e+00 | 1.2755e-15 | 1.5110e-16 | |
| &#39;ydot&#39; | &#39;theta&#39; | 8.5890e+00 | 8.5890e+00 | 2.0023e-15 | 2.3312e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;v&#39; | 1.5334e+00 | 1.5334e+00 | 2.2215e-16 | 1.4487e-16 | |
| &#39;ydot&#39; | &#39;v&#39; | 1.7623e+00 | 1.7623e+00 | 1.1102e-16 | 6.2998e-17 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+

##################################################################
Expand All @@ -752,7 +752,7 @@ <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;vdot&#39; | &#39;theta&#39; | 1.5960e+01 | 1.5960e+01 | 3.7682e-15 | 2.3610e-16 |
| &#39;check&#39; | &#39;theta&#39; | 9.4575e+02 | 9.4575e+02 | 3.5954e-13 | 3.8016e-16 |
+-----------------+------------------+-------------+-------------+-------------+-------------+
</pre></div>
</div>
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69 changes: 34 additions & 35 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-623a3844-cfd7-48fe-8330-964af6e3d975">
<span class="eqno">(21)<a class="headerlink" href="#equation-623a3844-cfd7-48fe-8330-964af6e3d975" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-9679a1f6-27f7-4115-b55f-252320874b23">
<span class="eqno">(21)<a class="headerlink" href="#equation-9679a1f6-27f7-4115-b55f-252320874b23" 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-c993a1a0-6221-481c-bdb5-a9bbc40f8a54">
<span class="eqno">(22)<a class="headerlink" href="#equation-c993a1a0-6221-481c-bdb5-a9bbc40f8a54" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-8fc2d51f-e2a6-4095-8a2d-08bf4e767854">
<span class="eqno">(22)<a class="headerlink" href="#equation-8fc2d51f-e2a6-4095-8a2d-08bf4e767854" 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-93757bc7-ec23-49c2-a00e-e01d4eb9a5f2">
<span class="eqno">(23)<a class="headerlink" href="#equation-93757bc7-ec23-49c2-a00e-e01d4eb9a5f2" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-2730c31e-c8ef-4e22-b9dd-831431a3a20a">
<span class="eqno">(23)<a class="headerlink" href="#equation-2730c31e-c8ef-4e22-b9dd-831431a3a20a" 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-ede7fbb3-834d-4fda-9228-abd8fabc28c5">
<span class="eqno">(24)<a class="headerlink" href="#equation-ede7fbb3-834d-4fda-9228-abd8fabc28c5" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-857d0635-165a-494c-9401-22dc147a6ce9">
<span class="eqno">(24)<a class="headerlink" href="#equation-857d0635-165a-494c-9401-22dc147a6ce9" 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-5a5a96b6-6dc7-414e-a130-ca7c7f0f756f">
<span class="eqno">(25)<a class="headerlink" href="#equation-5a5a96b6-6dc7-414e-a130-ca7c7f0f756f" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-1a3be642-7315-473e-b566-38c417d68b7d">
<span class="eqno">(25)<a class="headerlink" href="#equation-1a3be642-7315-473e-b566-38c417d68b7d" 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-d82c7f29-eb61-44f2-b4c6-8456e67f46f0">
<span class="eqno">(26)<a class="headerlink" href="#equation-d82c7f29-eb61-44f2-b4c6-8456e67f46f0" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-5e7941bc-f341-4415-af98-30367ba7c975">
<span class="eqno">(26)<a class="headerlink" href="#equation-5e7941bc-f341-4415-af98-30367ba7c975" 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 0x7fe2b0ebb580&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;dymos.phase.phase.Phase at 0x7ff1a4da78e0&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 @@ -1420,27 +1421,25 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Coloring for &#39;traj.phases.br_to_v1.rhs_all&#39; (class BalancedFieldODEComp)
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Jacobian shape: (132, 60) ( 9.80% nonzero)

Jacobian shape: (132, 60) ( 9.81% 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: 0.019714 sec.
Time to compute coloring: 0.015048 sec.
Time to compute sparsity: 0.025481 sec.
Time to compute coloring: 0.018218 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)

Jacobian shape: (132, 60) ( 9.80% nonzero)
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: 0.019854 sec.
Time to compute coloring: 0.014563 sec.
Time to compute sparsity: 0.025783 sec.
Time to compute coloring: 0.018428 sec.
Memory to compute coloring: 0.000000 MB.

Coloring for &#39;traj.phases.v1_to_vr.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1450,8 +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: 0.019551 sec.
Time to compute coloring: 0.014825 sec.
Time to compute sparsity: 0.026875 sec.
Time to compute coloring: 0.018604 sec.
Memory to compute coloring: 0.000000 MB.

Coloring for &#39;traj.phases.rotate.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1461,8 +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: 0.019517 sec.
Time to compute coloring: 0.014839 sec.
Time to compute sparsity: 0.025343 sec.
Time to compute coloring: 0.018415 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
Expand All @@ -1473,12 +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: 0.040785 sec.
Time to compute coloring: 0.030149 sec.
Time to compute sparsity: 0.053601 sec.
Time to compute coloring: 0.033164 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 1.376847 seconds.
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Full total jacobian was computed 3 times, taking 1.709031 seconds.
Total jacobian shape: (178, 166)


Expand All @@ -1487,8 +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: 1.376847 sec.
Time to compute coloring: 0.103024 sec.
Time to compute sparsity: 1.709031 sec.
Time to compute coloring: 0.120710 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
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32 changes: 16 additions & 16 deletions examples/balanced_field/balanced_field_funccomp.html
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Expand Up @@ -988,13 +988,13 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Coloring for &#39;traj.phases.br_to_v1.rhs_all&#39; (class ExplicitFuncComp)

Jacobian shape: (132, 60) ( 9.81% nonzero)
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: 0.345102 sec.
Time to compute coloring: 0.071380 sec.
Time to compute sparsity: 0.407177 sec.
Time to compute coloring: 0.084174 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
Expand All @@ -1003,13 +1003,13 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
</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 ExplicitFuncComp)

Jacobian shape: (132, 60) ( 9.77% nonzero)
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: 0.327971 sec.
Time to compute coloring: 0.071099 sec.
Time to compute sparsity: 0.379886 sec.
Time to compute coloring: 0.082436 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
Expand All @@ -1023,8 +1023,8 @@ <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: 0.329436 sec.
Time to compute coloring: 0.071868 sec.
Time to compute sparsity: 0.384563 sec.
Time to compute coloring: 0.085496 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
Expand All @@ -1038,8 +1038,8 @@ <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: 0.330049 sec.
Time to compute coloring: 0.072836 sec.
Time to compute sparsity: 0.386469 sec.
Time to compute coloring: 0.085052 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
Expand All @@ -1053,12 +1053,12 @@ <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: 0.434438 sec.
Time to compute coloring: 0.160801 sec.
Memory to compute coloring: 0.890625 MB.
Time to compute sparsity: 0.506151 sec.
Time to compute coloring: 0.190399 sec.
Memory to compute coloring: 0.574219 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 4.735711 seconds.
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Full total jacobian was computed 3 times, taking 5.520926 seconds.
Total jacobian shape: (178, 166)


Expand All @@ -1067,8 +1067,8 @@ <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: 4.735711 sec.
Time to compute coloring: 0.105743 sec.
Time to compute sparsity: 5.520926 sec.
Time to compute coloring: 0.123994 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
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