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bryanwweber committed Jun 16, 2024
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2 changes: 1 addition & 1 deletion _sources/time-since-periapsis-and-keplers-equation/universal-variables.md
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Expand Up @@ -312,7 +312,7 @@ The Laguerre algorithm can be implemented as:

:::{math}
:label:
\chi_{i + 1} = \chi_{i} - \frac{n f(\chi_i)}{f'(\chi_i) \pm \left[\left(n - 1\right)^2 \left(f'(\chi_i\right)^2 - n\left(n - 1\right) f(\chi_i)f''(\chi_i)\right]}
\chi_{i + 1} = \chi_{i} - \frac{n f(\chi_i)}{f'(\chi_i) \pm \left[\left(n - 1\right)^2 \left(f'(\chi_i)\right)^2 - n\left(n - 1\right) f(\chi_i)f''(\chi_i)\right]^{1/2}}
:::

The sign ambiguity in the denominator is determined by taking the sign of the numerical value of $f'(\chi_i)$. In addition, the solution is relatively insensitive to the choice of the value of $n$, which is an integer constant. It seems as though $n = 5$ is a reasonable value. Choosing $n = 1$ gives the standard Newton's algorithm.
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6 changes: 3 additions & 3 deletions classical-orbital-elements/classical-orbital-elements.html
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4 changes: 2 additions & 2 deletions interplanetary-maneuvers/planetary-arrival-capture.html
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2 changes: 1 addition & 1 deletion orbital-maneuvers/nonimpulsive-maneuver-example.html
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Expand Up @@ -709,7 +709,7 @@ <h2>Solution<a class="headerlink" href="#solution" title="Link to this heading">
</div>
</div>
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x7fd1e8a191f0&gt;]
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x7f207c4dd280&gt;]
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8 changes: 4 additions & 4 deletions orbital-maneuvers/plane-change-maneuvers.html
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2 changes: 1 addition & 1 deletion searchindex.js
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46 changes: 23 additions & 23 deletions the-n-body-problem/lagrange-points.html
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Expand Up @@ -800,42 +800,42 @@ <h2>Collinear Lagrange Points<a class="headerlink" href="#collinear-lagrange-poi
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Expand All @@ -845,9 +845,9 @@ <h2>Collinear Lagrange Points<a class="headerlink" href="#collinear-lagrange-poi
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Expand Down Expand Up @@ -140851,7 +140851,7 @@ <h2>Collinear Lagrange Points<a class="headerlink" href="#collinear-lagrange-poi
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46 changes: 23 additions & 23 deletions the-orbit-equation/hyperbolic-trajectories.html
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Expand Up @@ -698,42 +698,42 @@ <h1>Hyperbolic Trajectories (<span class="math notranslate nohighlight">\(e &gt;
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Expand All @@ -743,9 +743,9 @@ <h1>Hyperbolic Trajectories (<span class="math notranslate nohighlight">\(e &gt;
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Expand Down Expand Up @@ -161828,7 +161828,7 @@ <h1>Hyperbolic Trajectories (<span class="math notranslate nohighlight">\(e &gt;
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46 changes: 23 additions & 23 deletions time-since-periapsis-and-keplers-equation/time-since-periapsis.html
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Expand Up @@ -753,42 +753,42 @@ <h2>Mean and Eccentric Anomalies<a class="headerlink" href="#mean-and-eccentric-
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Expand All @@ -798,9 +798,9 @@ <h2>Mean and Eccentric Anomalies<a class="headerlink" href="#mean-and-eccentric-
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Expand Down Expand Up @@ -272786,7 +272786,7 @@ <h2>Mean and Eccentric Anomalies<a class="headerlink" href="#mean-and-eccentric-
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setTimeout(function() {
animb4135144bc3a46949bf9cdbacf747757 = new Animation(frames, img_id, slider_id, 16.0,
anim7a4974bc1a2c464db1b957df46be6fc4 = new Animation(frames, img_id, slider_id, 16.0,
loop_select_id);
}, 0);
})()
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