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16 changes: 8 additions & 8 deletions contributing/contributing.html
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Expand Up @@ -1055,21 +1055,21 @@ <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; | 2.0549e+02 | 2.0549e+02 | 3.1777e-14 | 1.5464e-16 | |
| &#39;check&#39; | &#39;theta&#39; | 5.2975e+01 | 5.2975e+01 | 3.5527e-15 | 6.7064e-17 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;check&#39; | &#39;v&#39; | 6.7274e+00 | 6.7274e+00 | 0.0000e+00 | 0.0000e+00 | |
| &#39;check&#39; | &#39;v&#39; | 4.1888e+00 | 4.1888e+00 | 0.0000e+00 | 0.0000e+00 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;theta&#39; | 1.2815e+01 | 1.2815e+01 | 9.1551e-16 | 7.1439e-17 | |
| &#39;vdot&#39; | &#39;theta&#39; | 1.4221e+01 | 1.4221e+01 | 2.1756e-15 | 1.5298e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;v&#39; | 0.0000e+00 | 0.0000e+00 | 0.0000e+00 | nan | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;theta&#39; | 1.4137e+01 | 1.4137e+01 | 1.2561e-15 | 8.8853e-17 | |
| &#39;xdot&#39; | &#39;theta&#39; | 1.0941e+01 | 1.0941e+01 | 9.9301e-16 | 9.0760e-17 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;v&#39; | 1.3068e+00 | 1.3068e+00 | 5.5511e-17 | 4.2479e-17 | |
| &#39;xdot&#39; | &#39;v&#39; | 1.4502e+00 | 1.4502e+00 | 9.6148e-17 | 6.6301e-17 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;theta&#39; | 9.6855e+00 | 9.6855e+00 | 9.9301e-16 | 1.0253e-16 | |
| &#39;ydot&#39; | &#39;theta&#39; | 9.9680e+00 | 9.9680e+00 | 1.0878e-15 | 1.0913e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;v&#39; | 1.8145e+00 | 1.8145e+00 | 1.1102e-16 | 6.1187e-17 | |
| &#39;ydot&#39; | &#39;v&#39; | 1.7021e+00 | 1.7021e+00 | 1.5701e-16 | 9.2247e-17 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+

##################################################################
Expand All @@ -1078,7 +1078,7 @@ <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;check&#39; | &#39;theta&#39; | 2.0549e+02 | 2.0549e+02 | 3.1777e-14 | 1.5464e-16 |
| &#39;vdot&#39; | &#39;theta&#39; | 1.4221e+01 | 1.4221e+01 | 2.1756e-15 | 1.5298e-16 |
+-----------------+------------------+-------------+-------------+-------------+-------------+
</pre></div>
</div>
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74 changes: 34 additions & 40 deletions examples/balanced_field/balanced_field.html
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Expand Up @@ -941,13 +941,13 @@ <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-09a00a34-9e5d-4a79-a126-a45d53e039da">
<span class="eqno">(21)<a class="headerlink" href="#equation-09a00a34-9e5d-4a79-a126-a45d53e039da" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-3228f40e-a586-447d-ab14-2e607fd5e6f5">
<span class="eqno">(21)<a class="headerlink" href="#equation-3228f40e-a586-447d-ab14-2e607fd5e6f5" 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-e6cd8392-3912-476d-80b8-bc47422f2752">
<span class="eqno">(22)<a class="headerlink" href="#equation-e6cd8392-3912-476d-80b8-bc47422f2752" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-ec5c7ed7-9b80-40cd-8286-c8f9a802e6e4">
<span class="eqno">(22)<a class="headerlink" href="#equation-ec5c7ed7-9b80-40cd-8286-c8f9a802e6e4" 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 @@ -956,8 +956,8 @@ <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-df6958a5-0516-4ccd-a65a-cf9207beecb3">
<span class="eqno">(23)<a class="headerlink" href="#equation-df6958a5-0516-4ccd-a65a-cf9207beecb3" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-a7c34d59-09b7-498a-b5f2-8c3d78a8d9f8">
<span class="eqno">(23)<a class="headerlink" href="#equation-a7c34d59-09b7-498a-b5f2-8c3d78a8d9f8" 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 @@ -968,17 +968,17 @@ <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-a957b5c8-24a0-4fd6-a246-96ed04afe83e">
<span class="eqno">(24)<a class="headerlink" href="#equation-a957b5c8-24a0-4fd6-a246-96ed04afe83e" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-3623ff3f-07af-45b2-a8b9-999f6551ec3d">
<span class="eqno">(24)<a class="headerlink" href="#equation-3623ff3f-07af-45b2-a8b9-999f6551ec3d" 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-75674819-6c20-4fbc-b3a7-3103d3f5ae48">
<span class="eqno">(25)<a class="headerlink" href="#equation-75674819-6c20-4fbc-b3a7-3103d3f5ae48" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-91cf6228-cb2d-46aa-a6ae-01b4dcb7879f">
<span class="eqno">(25)<a class="headerlink" href="#equation-91cf6228-cb2d-46aa-a6ae-01b4dcb7879f" 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 @@ -1005,8 +1005,8 @@ <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-272b4084-2d87-44cb-9c76-c0206c9bbc2f">
<span class="eqno">(26)<a class="headerlink" href="#equation-272b4084-2d87-44cb-9c76-c0206c9bbc2f" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-186c72c1-b75f-45d0-bb2e-7c0a8ce7d143">
<span class="eqno">(26)<a class="headerlink" href="#equation-186c72c1-b75f-45d0-bb2e-7c0a8ce7d143" 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 @@ -1531,7 +1531,7 @@ <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 0x7fae10155190&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;dymos.phase.phase.Phase at 0x7ff84ac73ed0&gt;
</pre></div>
</div>
</div>
Expand Down Expand Up @@ -1686,9 +1686,6 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>INFO: checking missing_recorders
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>WARNING: The Problem has no recorder of any kind attached
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>INFO: checking unserializable_options
</pre></div>
</div>
Expand All @@ -1714,9 +1711,6 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>INFO: checking missing_recorders
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>WARNING: The Problem has no recorder of any kind attached
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>INFO: checking unserializable_options
</pre></div>
</div>
Expand All @@ -1733,9 +1727,9 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.0162 sec
Time to compute coloring: 0.0105 sec
Memory to compute coloring: 0.2500 MB
Time to compute sparsity: 0.0160 sec
Time to compute coloring: 0.0103 sec
Memory to compute coloring: 0.1250 MB

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

Expand All @@ -1744,8 +1738,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.0161 sec
Time to compute coloring: 0.0102 sec
Time to compute sparsity: 0.0157 sec
Time to compute coloring: 0.0099 sec
Memory to compute coloring: 0.0000 MB

Coloring for &#39;traj.phases.v1_to_vr.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1755,8 +1749,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.0160 sec
Time to compute coloring: 0.0103 sec
Time to compute sparsity: 0.0157 sec
Time to compute coloring: 0.0100 sec
Memory to compute coloring: 0.0000 MB

Coloring for &#39;traj.phases.rotate.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1766,8 +1760,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.0162 sec
Time to compute coloring: 0.0103 sec
Time to compute sparsity: 0.0159 sec
Time to compute coloring: 0.0098 sec
Memory to compute coloring: 0.0000 MB

Coloring for &#39;traj.phases.climb.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1777,12 +1771,12 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 111 (85.59% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.0342 sec
Time to compute coloring: 0.0194 sec
Memory to compute coloring: 0.2500 MB
Time to compute sparsity: 0.0329 sec
Time to compute coloring: 0.0186 sec
Memory to compute coloring: 0.0000 MB
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Full total jacobian for problem &#39;problem&#39; was computed 3 times, taking 1.006189039999981 seconds.
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Full total jacobian for problem &#39;problem&#39; was computed 3 times, taking 0.9899345740000172 seconds.
Total jacobian shape: (178, 166)


Expand All @@ -1791,17 +1785,17 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 14 vs 166 (91.57% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 1.0062 sec
Time to compute coloring: 0.0684 sec
Time to compute sparsity: 0.9899 sec
Time to compute coloring: 0.0692 sec
Memory to compute coloring: 0.0000 MB
Coloring created on: 2024-09-24 15:27:06
Coloring created on: 2024-10-02 16:21:15
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/core/total_jac.py:1652: DerivativesWarning:Constraints or objectives [(&#39;traj.phases.climb-&gt;path_constraint-&gt;gam&#39;, inds=[(0, 0)])] cannot be impacted by the design variables of the problem.
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/core/group.py:1130: DerivativesWarning:Constraints or objectives [ode_eval.control_interp.control_rates:alpha_rate, ode_eval.control_interp.control_rates:alpha_rate2, ode_eval.control_interp.control_values:alpha] cannot be impacted by the design variables of the problem because no partials were defined for them in their parent component(s).
/usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/core/group.py:1130: DerivativesWarning:Constraints or objectives [ode_eval.control_interp.control_rates:alpha_rate, ode_eval.control_interp.control_rates:alpha_rate2, ode_eval.control_interp.control_values:alpha] cannot be impacted by the design variables of the problem because no partials were defined for them in their parent component(s).
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/core/group.py:1137: DerivativesWarning:Constraints or objectives [ode_eval.control_interp.control_rates:alpha_rate, ode_eval.control_interp.control_rates:alpha_rate2, ode_eval.control_interp.control_values:alpha] cannot be impacted by the design variables of the problem because no partials were defined for them in their parent component(s).
/usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/core/group.py:1137: DerivativesWarning:Constraints or objectives [ode_eval.control_interp.control_rates:alpha_rate, ode_eval.control_interp.control_rates:alpha_rate2, ode_eval.control_interp.control_values:alpha] cannot be impacted by the design variables of the problem because no partials were defined for them in their parent component(s).
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Simulating trajectory traj
Expand All @@ -1815,11 +1809,11 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Driver: pyOptSparseDriver
success : True
iterations : 25
runtime : 3.1670E+00 s
runtime : 3.0181E+00 s
model_evals : 25
model_time : 7.4630E-02 s
model_time : 7.1800E-02 s
deriv_evals : 24
deriv_time : 1.1940E+00 s
deriv_time : 1.1569E+00 s
exit_status : SUCCESS
</pre></div>
</div>
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