build based on 651e8ad

latest/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.11.2","generation_timestamp":"2024-12-12T16:47:47","documenter_version":"1.8.0"}}
+{"documenter":{"julia_version":"1.11.2","generation_timestamp":"2024-12-12T17:11:11","documenter_version":"1.8.0"}}

latest/abc_flow/index.html

@@ -9,8 +9,8 @@
 for solution in ensemble_solution
     plot!(p, solution.q[:, 1], solution.q[:, 2], solution.q[:, 3])
 end
-p</code></pre><img src="64aa6f7b.svg" alt="Example block output"/><h2 id="Library-functions"><a class="docs-heading-anchor" href="#Library-functions">Library functions</a><a id="Library-functions-1"></a><a class="docs-heading-anchor-permalink" href="#Library-functions" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="GeometricProblems.ABCFlow" href="#GeometricProblems.ABCFlow"><code>GeometricProblems.ABCFlow</code></a> — <span class="docstring-category">Module</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p><strong>ABC Flow</strong></p><p class="math-container">\[\begin{aligned}
+p</code></pre><img src="2cfadc35.svg" alt="Example block output"/><h2 id="Library-functions"><a class="docs-heading-anchor" href="#Library-functions">Library functions</a><a id="Library-functions-1"></a><a class="docs-heading-anchor-permalink" href="#Library-functions" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="GeometricProblems.ABCFlow" href="#GeometricProblems.ABCFlow"><code>GeometricProblems.ABCFlow</code></a> — <span class="docstring-category">Module</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p><strong>ABC Flow</strong></p><p class="math-container">\[\begin{aligned}
     \dot{x} = A\sin(z) + C\cos(y) \\
     \dot{y} = B\sin(x) + A\cos(z) \\ 
     \dot{z} = C\sin(y) + B\cos(x)
-\end{aligned}\]</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaGNI/GeometricProblems.jl/blob/b3c9fbec777c32a5d8a2c0555258c0ebad622730/src/abc_flow.jl#L1-L11">source</a></section></article><div class="citation canonical"><dl><dt>[1]</dt><dd><div id="hairer2006geometric">E. Hairer, C. Lubich and G. Wanner. <em>Geometric Numerical integration: structure-preserving algorithms for ordinary differential equations</em> (Springer, Berlin, 2006).</div></dd></dl></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../diagnostics/">« Diagnostics</a><a class="docs-footer-nextpage" href="../coupled_harmonic_oscillator/">Coupled Harmonic Oscillator »</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 1.8.0 on <span class="colophon-date" title="Thursday 12 December 2024 16:47">Thursday 12 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+\end{aligned}\]</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaGNI/GeometricProblems.jl/blob/651e8ad67a6d233a75c23d6f1a7241dda7b5f834/src/abc_flow.jl#L1-L11">source</a></section></article><div class="citation canonical"><dl><dt>[1]</dt><dd><div id="hairer2006geometric">E. Hairer, C. Lubich and G. Wanner. <em>Geometric Numerical integration: structure-preserving algorithms for ordinary differential equations</em> (Springer, Berlin, 2006).</div></dd></dl></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../diagnostics/">« Diagnostics</a><a class="docs-footer-nextpage" href="../coupled_harmonic_oscillator/">Coupled Harmonic Oscillator »</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 1.8.0 on <span class="colophon-date" title="Thursday 12 December 2024 17:11">Thursday 12 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

latest/double_pendulum/index.html

@@ -20,16 +20,16 @@
 \end{align*}\]</p><p>the Hamiltonian can be obtained via the Legendre transform,</p><p class="math-container">\[H = \sum_{i=1}^2 \dot{\theta}_i p_i - L ,\]</p><p>as</p><p class="math-container">\[\begin{align*}
 H &amp;= \frac{m_2 l_2^2 p^2_{\theta_1} + (m_1 + m_2) l_1^2 p^2_{\theta_2} - 2 m_2 l_1 l_2 p_{\theta_1} p_{\theta_2} \cos(\theta_1 - \theta_2)}{2 m_2 l_1^2 l_2^2 \left[ m_1 + m_2 \sin^2(\theta_1 - \theta_2) \right] } \\
   &amp; \qquad\qquad \vphantom{\frac{l}{l}} - g (m_1 + m_2) l_1 \cos\theta_1 - g m_2 l_2 \cos\theta_2 .
-\end{align*}\]</p><h2 id="Library-functions"><a class="docs-heading-anchor" href="#Library-functions">Library functions</a><a id="Library-functions-1"></a><a class="docs-heading-anchor-permalink" href="#Library-functions" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="GeometricProblems.DoublePendulum" href="#GeometricProblems.DoublePendulum"><code>GeometricProblems.DoublePendulum</code></a> — <span class="docstring-category">Module</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">DoublePendulum</code></pre><p>The <code>DoublePendulum</code> module provides functions <code>hodeproblem</code> and <code>lodeproblem</code> each returning a Hamiltonian or Lagrangian problem, respectively, to be solved in the GeometricIntegrators.jl ecosystem. The actual code is generated with EulerLagrange.jl.</p><p>The double pendulum consists of two pendula, one attached to the origin at <span>$(x,y) = (0,0)$</span>, and the second attached to the first. Each pendulum consists of a point mass <span>$m_i$</span> attached to a massless rod of length <span>$l_i$</span> with <span>$i \in (1,2)$</span>. The dynamics of the system is described in terms of the angles <span>$\theta_i$</span> between the rods <span>$l_i$</span> and the vertical axis <span>$y$</span>. All motion is assumed to be frictionless.</p><p>System parameters:</p><ul><li><code>l₁</code>: length of rod 1</li><li><code>l₂</code>: length of rod 2</li><li><code>m₁</code>: mass of pendulum 1</li><li><code>m₂</code>: mass of pendulum 2</li><li><code>g</code>: gravitational constant</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaGNI/GeometricProblems.jl/blob/b3c9fbec777c32a5d8a2c0555258c0ebad622730/src/double_pendulum.jl#L1-L22">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="GeometricProblems.DoublePendulum.hodeproblem" href="#GeometricProblems.DoublePendulum.hodeproblem"><code>GeometricProblems.DoublePendulum.hodeproblem</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Hamiltonian problem for the double pendulum</code></pre><p>Constructor with default arguments:</p><pre><code class="nohighlight hljs">hodeproblem(
+\end{align*}\]</p><h2 id="Library-functions"><a class="docs-heading-anchor" href="#Library-functions">Library functions</a><a id="Library-functions-1"></a><a class="docs-heading-anchor-permalink" href="#Library-functions" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="GeometricProblems.DoublePendulum" href="#GeometricProblems.DoublePendulum"><code>GeometricProblems.DoublePendulum</code></a> — <span class="docstring-category">Module</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">DoublePendulum</code></pre><p>The <code>DoublePendulum</code> module provides functions <code>hodeproblem</code> and <code>lodeproblem</code> each returning a Hamiltonian or Lagrangian problem, respectively, to be solved in the GeometricIntegrators.jl ecosystem. The actual code is generated with EulerLagrange.jl.</p><p>The double pendulum consists of two pendula, one attached to the origin at <span>$(x,y) = (0,0)$</span>, and the second attached to the first. Each pendulum consists of a point mass <span>$m_i$</span> attached to a massless rod of length <span>$l_i$</span> with <span>$i \in (1,2)$</span>. The dynamics of the system is described in terms of the angles <span>$\theta_i$</span> between the rods <span>$l_i$</span> and the vertical axis <span>$y$</span>. All motion is assumed to be frictionless.</p><p>System parameters:</p><ul><li><code>l₁</code>: length of rod 1</li><li><code>l₂</code>: length of rod 2</li><li><code>m₁</code>: mass of pendulum 1</li><li><code>m₂</code>: mass of pendulum 2</li><li><code>g</code>: gravitational constant</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaGNI/GeometricProblems.jl/blob/651e8ad67a6d233a75c23d6f1a7241dda7b5f834/src/double_pendulum.jl#L1-L22">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="GeometricProblems.DoublePendulum.hodeproblem" href="#GeometricProblems.DoublePendulum.hodeproblem"><code>GeometricProblems.DoublePendulum.hodeproblem</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Hamiltonian problem for the double pendulum</code></pre><p>Constructor with default arguments:</p><pre><code class="nohighlight hljs">hodeproblem(
     q₀ = [π/4, π/2],
     p₀ = [3.3321622036187746, 7.0685834705770345];
     tspan = (0.0, 10.0),
     tstep = 0.01,
     params = (l₁ = 2.0, l₂ = 3.0, m₁ = 1.0, m₂ = 2.0, g = 9.80665)
-)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaGNI/GeometricProblems.jl/blob/b3c9fbec777c32a5d8a2c0555258c0ebad622730/src/double_pendulum.jl#L105-L118">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="GeometricProblems.DoublePendulum.lodeproblem" href="#GeometricProblems.DoublePendulum.lodeproblem"><code>GeometricProblems.DoublePendulum.lodeproblem</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Lagrangian problem for the double pendulum</code></pre><p>Constructor with default arguments:</p><pre><code class="nohighlight hljs">lodeproblem(
+)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaGNI/GeometricProblems.jl/blob/651e8ad67a6d233a75c23d6f1a7241dda7b5f834/src/double_pendulum.jl#L105-L118">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="GeometricProblems.DoublePendulum.lodeproblem" href="#GeometricProblems.DoublePendulum.lodeproblem"><code>GeometricProblems.DoublePendulum.lodeproblem</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">Lagrangian problem for the double pendulum</code></pre><p>Constructor with default arguments:</p><pre><code class="nohighlight hljs">lodeproblem(
     q₀ = [π/4, π/2],
     p₀ = [3.3321622036187746, 7.0685834705770345];
     tspan = (0.0, 10.0),
     tstep = 0.01,
     params = (l₁ = 2.0, l₂ = 3.0, m₁ = 1.0, m₂ = 2.0, g = 9.80665)
-)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaGNI/GeometricProblems.jl/blob/b3c9fbec777c32a5d8a2c0555258c0ebad622730/src/double_pendulum.jl#L126-L139">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../coupled_harmonic_oscillator/">« Coupled Harmonic Oscillator</a><a class="docs-footer-nextpage" href="../harmonic_oscillator/">Harmonic Oscillator »</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 1.8.0 on <span class="colophon-date" title="Thursday 12 December 2024 16:47">Thursday 12 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaGNI/GeometricProblems.jl/blob/651e8ad67a6d233a75c23d6f1a7241dda7b5f834/src/double_pendulum.jl#L126-L139">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../coupled_harmonic_oscillator/">« Coupled Harmonic Oscillator</a><a class="docs-footer-nextpage" href="../harmonic_oscillator/">Harmonic Oscillator »</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 1.8.0 on <span class="colophon-date" title="Thursday 12 December 2024 17:11">Thursday 12 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>