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2 changes: 1 addition & 1 deletion _modules/dymos/trajectory/trajectory.html
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Expand Up @@ -1607,7 +1607,7 @@ <h1>Source code for dymos.trajectory.trajectory</h1><div class="highlight"><pre>
<span class="sd"> phases : sequence of str</span>
<span class="sd"> The names of the phases in this trajectory to be sequentially linked.</span>
<span class="sd"> vars : sequence of str</span>
<span class="sd"> The variables in the phases to be linked, or &#39;*&#39;. Providing &#39;*&#39; will time and all</span>
<span class="sd"> The variables in the phases to be linked, or &#39;*&#39;. Providing &#39;*&#39; will link time and all</span>
<span class="sd"> states. Linking control values or rates requires them to be listed explicitly.</span>
<span class="sd"> locs : tuple of str</span>
<span class="sd"> A two-element tuple of a location specification. For every pair in</span>
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2 changes: 1 addition & 1 deletion api/trajectory_api.html
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Expand Up @@ -699,7 +699,7 @@ <h2>link_phases<a class="headerlink" href="#link-phases" title="Permalink to thi
<dd class="field-odd"><dl class="simple">
<dt><strong>phases</strong><span class="classifier">sequence of str</span></dt><dd><p>The names of the phases in this trajectory to be sequentially linked.</p>
</dd>
<dt><strong>vars</strong><span class="classifier">sequence of str</span></dt><dd><p>The variables in the phases to be linked, or ‘*’. Providing ‘*’ will time and all
<dt><strong>vars</strong><span class="classifier">sequence of str</span></dt><dd><p>The variables in the phases to be linked, or ‘*’. Providing ‘*’ will link time and all
states. Linking control values or rates requires them to be listed explicitly.</p>
</dd>
<dt><strong>locs</strong><span class="classifier">tuple of str</span></dt><dd><p>A two-element tuple of a location specification. For every pair in
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16 changes: 8 additions & 8 deletions contributing/contributing.html
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Expand Up @@ -731,21 +731,21 @@ <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; | 3.5602e+01 | 3.5602e+01 | 9.9650e-16 | 2.7990e-17 | |
| &#39;check&#39; | &#39;theta&#39; | 3.0756e+01 | 3.0756e+01 | 3.9732e-15 | 1.2918e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;check&#39; | &#39;v&#39; | 3.2643e+00 | 3.2643e+00 | 5.4390e-16 | 1.6662e-16 | |
| &#39;check&#39; | &#39;v&#39; | 3.1106e+00 | 3.1106e+00 | 2.2204e-16 | 7.1382e-17 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;theta&#39; | 1.8530e+01 | 1.8530e+01 | 3.9721e-15 | 2.1436e-16 | |
| &#39;vdot&#39; | &#39;theta&#39; | 1.7943e+01 | 1.7943e+01 | 3.2024e-15 | 1.7847e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;v&#39; | 0.0000e+00 | 0.0000e+00 | 0.0000e+00 | nan | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;theta&#39; | 6.6754e+00 | 6.6754e+00 | 9.1552e-16 | 1.3715e-16 | |
| &#39;xdot&#39; | &#39;theta&#39; | 7.8496e+00 | 7.8496e+00 | 9.9340e-16 | 1.2655e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;v&#39; | 1.8895e+00 | 1.8895e+00 | 2.4825e-16 | 1.3139e-16 | |
| &#39;xdot&#39; | &#39;v&#39; | 1.8297e+00 | 1.8297e+00 | 3.3766e-16 | 1.8454e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;theta&#39; | 1.0161e+01 | 1.0161e+01 | 1.3506e-15 | 1.3292e-16 | |
| &#39;ydot&#39; | &#39;theta&#39; | 8.7498e+00 | 8.7498e+00 | 1.4906e-15 | 1.7035e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;v&#39; | 1.1957e+00 | 1.1957e+00 | 1.2413e-16 | 1.0381e-16 | |
| &#39;ydot&#39; | &#39;v&#39; | 1.2854e+00 | 1.2854e+00 | 2.0015e-16 | 1.5571e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+

##################################################################
Expand All @@ -754,7 +754,7 @@ <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; | 1.8530e+01 | 1.8530e+01 | 3.9721e-15 | 2.1436e-16 |
| &#39;xdot&#39; | &#39;v&#39; | 1.8297e+00 | 1.8297e+00 | 3.3766e-16 | 1.8454e-16 |
+-----------------+------------------+-------------+-------------+-------------+-------------+
</pre></div>
</div>
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64 changes: 32 additions & 32 deletions examples/balanced_field/balanced_field.html
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Expand Up @@ -577,13 +577,13 @@ <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-43504572-dbeb-4607-b6c6-4de01afe52a2">
<span class="eqno">(21)<a class="headerlink" href="#equation-43504572-dbeb-4607-b6c6-4de01afe52a2" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-3f29803c-0a04-4f18-80d9-352bad103035">
<span class="eqno">(21)<a class="headerlink" href="#equation-3f29803c-0a04-4f18-80d9-352bad103035" 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-ff8302b6-42ab-4d19-8024-b0bd515c5433">
<span class="eqno">(22)<a class="headerlink" href="#equation-ff8302b6-42ab-4d19-8024-b0bd515c5433" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-edfeff0c-53e8-4424-b53e-e04e40cf771f">
<span class="eqno">(22)<a class="headerlink" href="#equation-edfeff0c-53e8-4424-b53e-e04e40cf771f" 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 @@ -592,8 +592,8 @@ <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-818e775e-a294-4e71-8445-9cfead3611bd">
<span class="eqno">(23)<a class="headerlink" href="#equation-818e775e-a294-4e71-8445-9cfead3611bd" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-b0999a25-c3fa-4f9f-b2b7-df18fb3a8660">
<span class="eqno">(23)<a class="headerlink" href="#equation-b0999a25-c3fa-4f9f-b2b7-df18fb3a8660" 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 @@ -604,17 +604,17 @@ <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-e6b63053-7e5e-4a6d-bf30-fdab9ca50888">
<span class="eqno">(24)<a class="headerlink" href="#equation-e6b63053-7e5e-4a6d-bf30-fdab9ca50888" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-90b01ca7-b725-4fd6-b0c9-2ac7abe0ef6b">
<span class="eqno">(24)<a class="headerlink" href="#equation-90b01ca7-b725-4fd6-b0c9-2ac7abe0ef6b" 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-3c268cb2-d21a-408e-98c4-4179c1dd834d">
<span class="eqno">(25)<a class="headerlink" href="#equation-3c268cb2-d21a-408e-98c4-4179c1dd834d" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-f108d6e0-56ee-46bd-989e-8bcbad95d73c">
<span class="eqno">(25)<a class="headerlink" href="#equation-f108d6e0-56ee-46bd-989e-8bcbad95d73c" 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 @@ -641,8 +641,8 @@ <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-ae32dbe8-8e80-4f57-a363-d145903d1ce8">
<span class="eqno">(26)<a class="headerlink" href="#equation-ae32dbe8-8e80-4f57-a363-d145903d1ce8" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-66c2619a-05ec-411b-af07-ef1ba8a80b0d">
<span class="eqno">(26)<a class="headerlink" href="#equation-66c2619a-05ec-411b-af07-ef1ba8a80b0d" 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 @@ -1166,7 +1166,7 @@ <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 0x7f97acc620e0&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;dymos.phase.phase.Phase at 0x7fb5f82aa7a0&gt;
</pre></div>
</div>
</div>
Expand Down Expand Up @@ -1318,9 +1318,8 @@ <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]
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>INFO: checking out_of_order

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 @@ -1436,19 +1435,20 @@ <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: 0.023771 sec.
Time to compute coloring: 0.017591 sec.
Time to compute sparsity: 0.020226 sec.
Time to compute coloring: 0.015247 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) ( 9.75% 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: 0.023926 sec.
Time to compute coloring: 0.016634 sec.
Time to compute sparsity: 0.021794 sec.
Time to compute coloring: 0.015750 sec.
Memory to compute coloring: 0.000000 MB.

Coloring for &#39;traj.phases.v1_to_vr.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1458,8 +1458,8 @@ <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: 0.023504 sec.
Time to compute coloring: 0.017441 sec.
Time to compute sparsity: 0.019958 sec.
Time to compute coloring: 0.014951 sec.
Memory to compute coloring: 0.000000 MB.

Coloring for &#39;traj.phases.rotate.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1469,8 +1469,8 @@ <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: 0.023450 sec.
Time to compute coloring: 0.016833 sec.
Time to compute sparsity: 0.019837 sec.
Time to compute coloring: 0.015025 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
Expand All @@ -1481,12 +1481,12 @@ <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: 0.049618 sec.
Time to compute coloring: 0.033681 sec.
Time to compute sparsity: 0.041379 sec.
Time to compute coloring: 0.029963 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 1.739460 seconds.
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Full total jacobian was computed 3 times, taking 1.337170 seconds.
Total jacobian shape: (178, 166)


Expand All @@ -1495,8 +1495,8 @@ <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: 1.739460 sec.
Time to compute coloring: 0.122413 sec.
Time to compute sparsity: 1.337170 sec.
Time to compute coloring: 0.103963 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
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