build based on 16fde73

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-08-18T10:02:03","documenter_version":"1.5.0"}}
+{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-08-18T10:15:48","documenter_version":"1.5.0"}}

dev/examples/index.html

@@ -67,17 +67,22 @@
 for i in 1:segments
     UNIT_VECTORS0[:, i] .= [0, 0, 1.0]
     SEGMENTS0[:, i] .= POS0[:, i+1] - POS0[:, i]
-end</code></pre><p>The first example of such a model is the script <a href="https://github.com/ufechner7/Tethers.jl/blob/main/src/Tether_04.jl">Tether_04.jl</a> which is derived from the last example.</p><h2 id="Segmented-tether-with-correct-force-distribution"><a class="docs-heading-anchor" href="#Segmented-tether-with-correct-force-distribution">Segmented tether with correct force distribution</a><a id="Segmented-tether-with-correct-force-distribution-1"></a><a class="docs-heading-anchor-permalink" href="#Segmented-tether-with-correct-force-distribution" title="Permalink"></a></h2><p>In the script <a href="https://github.com/ufechner7/Tethers.jl/blob/main/src/Tether_05.jl#L61">Tether_05.jl</a>, the spring force is distributed correctly on the two masses attached to the spring as shown here:</p><pre><code class="language-julia hljs">    if i == segments
-        push!(eqs, total_force[:, i+1] ~ spring_force[:, i])
-        push!(eqs, acc[:, i+1]         ~ G_EARTH + total_force[:, i+1] / (0.5 * mass))
-        push!(eqs, total_force[:, i]   ~ spring_force[:, i-1] - spring_force[:, i])
+end</code></pre><p>The first example of such a model is the script <a href="https://github.com/ufechner7/Tethers.jl/blob/main/src/Tether_04.jl">Tether_04.jl</a> which is derived from the last example.</p><h2 id="Segmented-tether-with-correct-force-distribution"><a class="docs-heading-anchor" href="#Segmented-tether-with-correct-force-distribution">Segmented tether with correct force distribution</a><a id="Segmented-tether-with-correct-force-distribution-1"></a><a class="docs-heading-anchor-permalink" href="#Segmented-tether-with-correct-force-distribution" title="Permalink"></a></h2><p>In the script <a href="https://github.com/ufechner7/Tethers.jl/blob/main/src/Tether_05.jl#L61">Tether_05.jl</a>, the spring force is distributed correctly on the two masses attached to the spring as shown here:</p><pre><code class="language-julia hljs"># loop over all tether particles to apply the forces and calculate the accelerations
+for i in 1:(segments+1)
+    global eqs2; local eqs
+    eqs = []
+    if i == segments+1
+        push!(eqs, total_force[:, i] ~ spring_force[:, i-1])
+        push!(eqs, acc[:, i]         ~ G_EARTH + total_force[:, i] / (0.5 * mass))
     elseif i == 1
-        push!(eqs, total_force[:, i]   ~ spring_force[:, i])
-        push!(eqs, acc[:, i+1]         ~ G_EARTH + total_force[:, i+1] / mass)
+        push!(eqs, total_force[:, i] ~ spring_force[:, i])
+        push!(eqs, acc[:, i]         ~ zeros(3))
     else
         push!(eqs, total_force[:, i] ~ spring_force[:, i-1] - spring_force[:, i])
-        push!(eqs, acc[:, i+1]       ~ G_EARTH + total_force[:, i+1] / mass)
-    end</code></pre><p>We loop backward over the segments. For the last segment we calculate the force at both of its particles,  starting with the last particle, because on the last particle, only one force is acting.  On particle <span>$n-1$</span> two spring forces are acting in the opposite direction.</p><p><strong>Julia code:</strong> <a href="https://github.com/ufechner7/Tethers.jl/blob/main/src/Tether_05.jl">Tether_05.jl</a></p><p><strong>Python code:</strong> <a href="https://github.com/ufechner7/Tethers.jl/blob/main/src/Tether_05.py">Tether_05.py</a></p><p>Finally, in this example, we plot the result dynamically as 2D video. Screenshot:</p><p><img src="../docs/images/Tether2d.png" alt="Tether 2D"/></p><h2 id="Multi-segment-tether-reeling-out"><a class="docs-heading-anchor" href="#Multi-segment-tether-reeling-out">Multi-segment tether reeling out</a><a id="Multi-segment-tether-reeling-out-1"></a><a class="docs-heading-anchor-permalink" href="#Multi-segment-tether-reeling-out" title="Permalink"></a></h2><p>In this example, we assume a constant reel-out speed of <span>$V_{RO}=2m/s$</span>. When reeling out the following values need to be dynamically calculated:</p><ul><li>unstretched length of a tether segment</li><li>mass of the tether segment</li><li>spring constant</li><li>damping constant</li></ul><p>We do this in the following way at <a href="https://github.com/ufechner7/Tethers.jl/blob/87635d9df32f3ded49d0a394b613b412c2c83d55/src/Tether_06.jl#L76C1-L79C59">line 76ff</a>:</p><pre><code class="language-julia hljs">length            ~ L0 + V_RO*t 
+        push!(eqs, acc[:, i]         ~ G_EARTH + total_force[:, i] / mass)
+    end
+    eqs2 = vcat(eqs2, reduce(vcat, eqs))
+end</code></pre><p>We loop over the particles. The first and the last particle only one spring force is acting.  On the other particles two spring forces are acting in the opposite direction. Because the first particle is fixed we set its acceleration to zero.</p><p><strong>Julia code:</strong> <a href="https://github.com/ufechner7/Tethers.jl/blob/main/src/Tether_05.jl">Tether_05.jl</a></p><p><strong>Python code:</strong> <a href="https://github.com/ufechner7/Tethers.jl/blob/main/src/Tether_05.py">Tether_05.py</a></p><p>Finally, in this example, we plot the result dynamically as 2D video. Screenshot:</p><p><img src="../docs/images/Tether2d.png" alt="Tether 2D"/></p><h2 id="Multi-segment-tether-reeling-out"><a class="docs-heading-anchor" href="#Multi-segment-tether-reeling-out">Multi-segment tether reeling out</a><a id="Multi-segment-tether-reeling-out-1"></a><a class="docs-heading-anchor-permalink" href="#Multi-segment-tether-reeling-out" title="Permalink"></a></h2><p>In this example, we assume a constant reel-out speed of <span>$V_{RO}=2m/s$</span>. When reeling out the following values need to be dynamically calculated:</p><ul><li>unstretched length of a tether segment</li><li>mass of the tether segment</li><li>spring constant</li><li>damping constant</li></ul><p>We do this in the following way at <a href="https://github.com/ufechner7/Tethers.jl/blob/87635d9df32f3ded49d0a394b613b412c2c83d55/src/Tether_06.jl#L76C1-L79C59">line 76ff</a>:</p><pre><code class="language-julia hljs">length            ~ L0 + V_RO*t 
 m_tether_particle ~ mass_per_meter * (length/segments)
 c_spring          ~ C_SPRING / (length/segments)
 damping           ~ DAMPING  / (length/segments)</code></pre><p>where <code>L0</code> is the unstretched length of the complete tether at <span>$t=0$</span>. </p><p><strong>Julia code:</strong> <a href="https://github.com/ufechner7/Tethers.jl/blob/main/src/Tether_06.jl">Tether_06.jl</a></p><p>The IDA solver, used for Python has a very high numerical damping. Therefore we had to multiply the damping coefficient with a factor of <span>$0.045$</span> to achieve a more-or-less realistic result.</p><p><strong>Python code:</strong> <a href="https://github.com/ufechner7/Tethers.jl/blob/main/src/Tether_06.py">Tether_06.py</a></p><h3 id="Refactoring-the-code,-add-a-Settings-struct-and-splitting-it-into-functions"><a class="docs-heading-anchor" href="#Refactoring-the-code,-add-a-Settings-struct-and-splitting-it-into-functions">Refactoring the code, add a Settings struct and splitting it into functions</a><a id="Refactoring-the-code,-add-a-Settings-struct-and-splitting-it-into-functions-1"></a><a class="docs-heading-anchor-permalink" href="#Refactoring-the-code,-add-a-Settings-struct-and-splitting-it-into-functions" title="Permalink"></a></h3><p><strong>Julia code:</strong> <a href="https://github.com/ufechner7/Tethers.jl/blob/main/src/Tether_06b.jl">Tether_06b.jl</a>.</p><p>If you want to have fast code, that can be reused and tested using unit tests, then it is better to put your code in functions and to avoid global variables. We demonstrate that in this example.</p><p>First, the settings are stored in a <code>struct</code> type:</p><pre><code class="language-julia hljs">@with_kw mutable struct Settings @deftype Float64
@@ -113,4 +118,4 @@
 end
 @named sys = ODESystem(eqs, t; continuous_events = cb)</code></pre><h2 id="Segmented-tether-with-aerodynamic-drag"><a class="docs-heading-anchor" href="#Segmented-tether-with-aerodynamic-drag">Segmented tether with aerodynamic drag</a><a id="Segmented-tether-with-aerodynamic-drag-1"></a><a class="docs-heading-anchor-permalink" href="#Segmented-tether-with-aerodynamic-drag" title="Permalink"></a></h2><p>In the script <a href="https://github.com/ufechner7/Tethers.jl/blob/main/src/Tether_07.jl">Tether_07.jl</a>, the tether drag has been added.</p><p>The following lines calculate the tether drag and add half of the drag force to the two particles at the end of each segment:</p><pre><code class="language-julia hljs">    v_app_perp[:, i]   ~ v_apparent[:, i] - (v_apparent[:, i] ⋅ unit_vector[:, i]) .* unit_vector[:, i],
     norm_v_app[i]      ~ norm(v_app_perp[:, i]),
-    half_drag_force[:, i] .~ 0.25 * se.rho * se.cd_tether * norm_v_app[i] * (norm1[i]*se.d_tether/1000.0)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../theory/">« Theory</a><a class="docs-footer-nextpage" href="../vscode/">VSCode IDE »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.5.0 on <span class="colophon-date" title="Sunday 18 August 2024 10:02">Sunday 18 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+    half_drag_force[:, i] .~ 0.25 * se.rho * se.cd_tether * norm_v_app[i] * (norm1[i]*se.d_tether/1000.0)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../theory/">« Theory</a><a class="docs-footer-nextpage" href="../vscode/">VSCode IDE »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.5.0 on <span class="colophon-date" title="Sunday 18 August 2024 10:15">Sunday 18 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>