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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<script type="text/javascript" defer
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<title>Inverted Pendulum Equation Viewer</title>
<style>
body {
font-family: 'Arial', sans-serif;
margin: 20px;
color: #333;
}
h1 {
text-align: center;
color: #444;
}
.control-container {
display: flex;
align-items: center;
justify-content: center;
margin-bottom: 20px;
}
.control-label {
font-weight: bold;
margin-right: 10px;
}
.arrow {
cursor: pointer;
font-size: 20px;
color: #555;
margin: 0 10px;
user-select: none; /* Prevent text selection */
border: 2px solid transparent; /* Prevent focus outline */
border-radius: 5px;
padding: 5px 10px;
transition: background-color 0.3s, color 0.3s;
}
.arrow:hover {
background-color: #007BFF;
color: white;
}
.arrow:active {
transform: scale(0.9);
}
.slider {
-webkit-appearance: none;
appearance: none;
width: 200px;
height: 8px;
background: #ddd;
border-radius: 5px;
outline: none;
transition: background 0.3s;
}
.slider:hover {
background: #ccc;
}
.slider::-webkit-slider-thumb {
-webkit-appearance: none;
appearance: none;
width: 16px;
height: 16px;
border-radius: 50%;
background: #007BFF;
cursor: pointer;
transition: background-color 0.3s, transform 0.2s;
}
.slider::-webkit-slider-thumb:hover {
background: #0056b3;
}
.slider::-webkit-slider-thumb:active {
transform: scale(1.2);
}
img {
max-width: 100%;
height: auto;
border: 1px solid #ddd;
border-radius: 4px;
padding: 5px;
display: block;
margin: 0 auto;
box-shadow: 0px 4px 10px rgba(0, 0, 0, 0.1);
}
</style>
</head>
<body>
<h1>Inverted Pendulum Viewer</h1>
<div class="latex-equation">
$$\begin{align*}
&\text{Original: } \ddot{\theta} + \frac{g}{l} \sin (\theta) = \frac{ A \omega^2}{l} \left( \cos (\theta) \cos(\omega t) \right)\\
&\text{First-Order: } \ddot{\theta} + \frac{g}{l}(\pi - \theta) = -\frac{ A \omega^2}{l}\cos(\omega t) \\
&\text{Second-Order: } \ddot{\theta} + \frac{g}{l}\left((\pi - \theta) + \frac{(\theta - \pi)^3}{6}\right) = \frac{ A \omega^2}{l}\left(-1 + \frac{(x-\pi)^2}{2}\right)\cos(\omega t)
\end{align*}$$
</div>
<div class="control-container">
<label class="control-label">\(A\):</label>
<span class="arrow" onclick="changeValue('A', -1)">←</span>
<span id="A-value">0.0</span>
<span class="arrow" onclick="changeValue('A', 1)">→</span>
<input id="A-slider" type="range" min="0" max="0" step="1" class="slider" oninput="updateSliderValue('A', this.value)">
</div>
<div class="control-container">
<label class="control-label">\(\omega\):</label>
<span class="arrow" onclick="changeValue('omega', -1)">←</span>
<span id="omega-value">0.0</span>
<span class="arrow" onclick="changeValue('omega', 1)">→</span>
<input id="omega-slider" type="range" min="0" max="0" step="1" class="slider" oninput="updateSliderValue('omega', this.value)">
</div>
<div class="control-container">
<label class="control-label">\(l\):</label>
<span class="arrow" onclick="changeValue('l', -1)">←</span>
<span id="l-value">0.0</span>
<span class="arrow" onclick="changeValue('l', 1)">→</span>
<input id="l-slider" type="range" min="0" max="0" step="1" class="slider" oninput="updateSliderValue('l', this.value)">
</div>
<div class="control-container">
<label class="control-label">\(\theta_0\):</label>
<span class="arrow" onclick="changeValue('theta_0', -1)">←</span>
<span id="theta_0-value">0.0</span>
<span class="arrow" onclick="changeValue('theta_0', 1)">→</span>
<input id="theta_0-slider" type="range" min="0" max="0" step="1" class="slider" oninput="updateSliderValue('theta_0', this.value)">
</div>
<div>
<img id="simulation-image" src="" alt="Simulation Image">
</div>
<script>
// Available images data
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"IP_COMPARISON_FIGURES/A_8.2_omega4.6_l_4.6_theta_0_3.166592653589793.svg"}, {"A": 4.6, "omega": 4.6, "l": 6.4, "theta_0": 3.066592653589793, "file": "IP_COMPARISON_FIGURES/A_4.6_omega4.6_l_6.4_theta_0_3.066592653589793.svg"}, {"A": 10.0, "omega": 6.4, "l": 8.2, "theta_0": 3.266592653589793, "file": "IP_COMPARISON_FIGURES/A_10.0_omega6.4_l_8.2_theta_0_3.266592653589793.svg"}, {"A": 8.2, "omega": 8.2, "l": 4.6, "theta_0": 3.266592653589793, "file": "IP_COMPARISON_FIGURES/A_8.2_omega8.2_l_4.6_theta_0_3.266592653589793.svg"}, {"A": 10.0, "omega": 2.8, "l": 8.2, "theta_0": 3.2165926535897933, "file": "IP_COMPARISON_FIGURES/A_10.0_omega2.8_l_8.2_theta_0_3.2165926535897933.svg"}, {"A": 8.2, "omega": 6.4, "l": 1.0, "theta_0": 3.016592653589793, "file": "IP_COMPARISON_FIGURES/A_8.2_omega6.4_l_1.0_theta_0_3.016592653589793.svg"}, {"A": 1.0, "omega": 1.0, "l": 10.0, "theta_0": 3.166592653589793, "file": "IP_COMPARISON_FIGURES/A_1.0_omega1.0_l_10.0_theta_0_3.166592653589793.svg"}, {"A": 2.8, 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"IP_COMPARISON_FIGURES/A_1.0_omega10.0_l_6.4_theta_0_3.116592653589793.svg"}, {"A": 6.4, "omega": 6.4, "l": 2.8, "theta_0": 3.2165926535897933, "file": "IP_COMPARISON_FIGURES/A_6.4_omega6.4_l_2.8_theta_0_3.2165926535897933.svg"}, {"A": 6.4, "omega": 1.0, "l": 1.0, "theta_0": 3.116592653589793, "file": "IP_COMPARISON_FIGURES/A_6.4_omega1.0_l_1.0_theta_0_3.116592653589793.svg"}, {"A": 1.0, "omega": 1.0, "l": 8.2, "theta_0": 3.066592653589793, "file": "IP_COMPARISON_FIGURES/A_1.0_omega1.0_l_8.2_theta_0_3.066592653589793.svg"}, {"A": 10.0, "omega": 4.6, "l": 2.8, "theta_0": 3.066592653589793, "file": "IP_COMPARISON_FIGURES/A_10.0_omega4.6_l_2.8_theta_0_3.066592653589793.svg"}, {"A": 8.2, "omega": 10.0, "l": 8.2, "theta_0": 3.166592653589793, "file": "IP_COMPARISON_FIGURES/A_8.2_omega10.0_l_8.2_theta_0_3.166592653589793.svg"}, {"A": 2.8, "omega": 10.0, "l": 6.4, "theta_0": 3.166592653589793, "file": "IP_COMPARISON_FIGURES/A_2.8_omega10.0_l_6.4_theta_0_3.166592653589793.svg"}, {"A": 1.0, "omega": 1.0, "l": 1.0, "theta_0": 3.266592653589793, "file": "IP_COMPARISON_FIGURES/A_1.0_omega1.0_l_1.0_theta_0_3.266592653589793.svg"}, {"A": 6.4, "omega": 4.6, "l": 6.4, "theta_0": 3.2165926535897933, "file": "IP_COMPARISON_FIGURES/A_6.4_omega4.6_l_6.4_theta_0_3.2165926535897933.svg"}, {"A": 8.2, "omega": 4.6, "l": 2.8, "theta_0": 3.016592653589793, "file": "IP_COMPARISON_FIGURES/A_8.2_omega4.6_l_2.8_theta_0_3.016592653589793.svg"}, {"A": 4.6, "omega": 1.0, "l": 1.0, "theta_0": 3.116592653589793, "file": "IP_COMPARISON_FIGURES/A_4.6_omega1.0_l_1.0_theta_0_3.116592653589793.svg"}, {"A": 1.0, "omega": 6.4, "l": 1.0, "theta_0": 3.2165926535897933, "file": "IP_COMPARISON_FIGURES/A_1.0_omega6.4_l_1.0_theta_0_3.2165926535897933.svg"}, {"A": 6.4, "omega": 1.0, "l": 6.4, "theta_0": 3.2165926535897933, "file": "IP_COMPARISON_FIGURES/A_6.4_omega1.0_l_6.4_theta_0_3.2165926535897933.svg"}, {"A": 10.0, "omega": 10.0, "l": 1.0, "theta_0": 3.2165926535897933, "file": "IP_COMPARISON_FIGURES/A_10.0_omega10.0_l_1.0_theta_0_3.2165926535897933.svg"}, {"A": 4.6, "omega": 1.0, "l": 10.0, "theta_0": 3.166592653589793, "file": "IP_COMPARISON_FIGURES/A_4.6_omega1.0_l_10.0_theta_0_3.166592653589793.svg"}, {"A": 1.0, "omega": 8.2, "l": 4.6, "theta_0": 3.2165926535897933, "file": "IP_COMPARISON_FIGURES/A_1.0_omega8.2_l_4.6_theta_0_3.2165926535897933.svg"}, {"A": 8.2, "omega": 6.4, "l": 2.8, "theta_0": 3.266592653589793, "file": "IP_COMPARISON_FIGURES/A_8.2_omega6.4_l_2.8_theta_0_3.266592653589793.svg"}, {"A": 8.2, "omega": 10.0, "l": 4.6, "theta_0": 3.066592653589793, "file": "IP_COMPARISON_FIGURES/A_8.2_omega10.0_l_4.6_theta_0_3.066592653589793.svg"}, {"A": 2.8, "omega": 6.4, "l": 6.4, "theta_0": 3.2165926535897933, "file": "IP_COMPARISON_FIGURES/A_2.8_omega6.4_l_6.4_theta_0_3.2165926535897933.svg"}, {"A": 2.8, "omega": 1.0, "l": 1.0, "theta_0": 3.016592653589793, "file": "IP_COMPARISON_FIGURES/A_2.8_omega1.0_l_1.0_theta_0_3.016592653589793.svg"}, {"A": 4.6, "omega": 4.6, "l": 10.0, "theta_0": 3.166592653589793, "file": "IP_COMPARISON_FIGURES/A_4.6_omega4.6_l_10.0_theta_0_3.166592653589793.svg"}, {"A": 6.4, "omega": 10.0, "l": 1.0, "theta_0": 3.266592653589793, "file": "IP_COMPARISON_FIGURES/A_6.4_omega10.0_l_1.0_theta_0_3.266592653589793.svg"}, {"A": 10.0, "omega": 2.8, "l": 6.4, "theta_0": 3.2165926535897933, "file": "IP_COMPARISON_FIGURES/A_10.0_omega2.8_l_6.4_theta_0_3.2165926535897933.svg"}, {"A": 6.4, "omega": 10.0, "l": 8.2, "theta_0": 3.066592653589793, "file": "IP_COMPARISON_FIGURES/A_6.4_omega10.0_l_8.2_theta_0_3.066592653589793.svg"}, {"A": 1.0, "omega": 10.0, "l": 10.0, "theta_0": 3.2165926535897933, "file": "IP_COMPARISON_FIGURES/A_1.0_omega10.0_l_10.0_theta_0_3.2165926535897933.svg"}, {"A": 2.8, "omega": 10.0, "l": 10.0, "theta_0": 3.266592653589793, "file": "IP_COMPARISON_FIGURES/A_2.8_omega10.0_l_10.0_theta_0_3.266592653589793.svg"}, {"A": 2.8, "omega": 4.6, "l": 2.8, "theta_0": 3.2165926535897933, "file": "IP_COMPARISON_FIGURES/A_2.8_omega4.6_l_2.8_theta_0_3.2165926535897933.svg"}, {"A": 1.0, "omega": 1.0, "l": 4.6, "theta_0": 3.166592653589793, "file": "IP_COMPARISON_FIGURES/A_1.0_omega1.0_l_4.6_theta_0_3.166592653589793.svg"}, {"A": 2.8, "omega": 1.0, "l": 2.8, "theta_0": 3.2165926535897933, "file": "IP_COMPARISON_FIGURES/A_2.8_omega1.0_l_2.8_theta_0_3.2165926535897933.svg"}, {"A": 2.8, "omega": 4.6, "l": 2.8, "theta_0": 3.016592653589793, "file": "IP_COMPARISON_FIGURES/A_2.8_omega4.6_l_2.8_theta_0_3.016592653589793.svg"}, {"A": 4.6, "omega": 10.0, "l": 2.8, "theta_0": 3.066592653589793, "file": "IP_COMPARISON_FIGURES/A_4.6_omega10.0_l_2.8_theta_0_3.066592653589793.svg"}, {"A": 1.0, "omega": 6.4, "l": 2.8, "theta_0": 3.016592653589793, "file": "IP_COMPARISON_FIGURES/A_1.0_omega6.4_l_2.8_theta_0_3.016592653589793.svg"}, {"A": 6.4, "omega": 1.0, "l": 2.8, "theta_0": 3.2165926535897933, "file": "IP_COMPARISON_FIGURES/A_6.4_omega1.0_l_2.8_theta_0_3.2165926535897933.svg"}, {"A": 2.8, "omega": 10.0, "l": 8.2, "theta_0": 3.066592653589793, "file": "IP_COMPARISON_FIGURES/A_2.8_omega10.0_l_8.2_theta_0_3.066592653589793.svg"}, {"A": 8.2, "omega": 10.0, "l": 6.4, "theta_0": 3.066592653589793, "file": "IP_COMPARISON_FIGURES/A_8.2_omega10.0_l_6.4_theta_0_3.066592653589793.svg"}, {"A": 6.4, "omega": 4.6, "l": 2.8, "theta_0": 3.2165926535897933, "file": "IP_COMPARISON_FIGURES/A_6.4_omega4.6_l_2.8_theta_0_3.2165926535897933.svg"}, {"A": 1.0, "omega": 4.6, "l": 1.0, "theta_0": 3.2165926535897933, "file": "IP_COMPARISON_FIGURES/A_1.0_omega4.6_l_1.0_theta_0_3.2165926535897933.svg"}, {"A": 2.8, "omega": 10.0, "l": 1.0, "theta_0": 3.266592653589793, "file": "IP_COMPARISON_FIGURES/A_2.8_omega10.0_l_1.0_theta_0_3.266592653589793.svg"}, {"A": 1.0, "omega": 1.0, "l": 6.4, "theta_0": 3.166592653589793, "file": "IP_COMPARISON_FIGURES/A_1.0_omega1.0_l_6.4_theta_0_3.166592653589793.svg"}, {"A": 1.0, "omega": 10.0, "l": 8.2, "theta_0": 3.016592653589793, "file": "IP_COMPARISON_FIGURES/A_1.0_omega10.0_l_8.2_theta_0_3.016592653589793.svg"}, {"A": 1.0, "omega": 1.0, "l": 1.0, "theta_0": 3.2165926535897933, "file": "IP_COMPARISON_FIGURES/A_1.0_omega1.0_l_1.0_theta_0_3.2165926535897933.svg"}, {"A": 6.4, "omega": 6.4, "l": 6.4, "theta_0": 3.2165926535897933, "file": "IP_COMPARISON_FIGURES/A_6.4_omega6.4_l_6.4_theta_0_3.2165926535897933.svg"}];
// Get unique values for each parameter
const uniqueValues = {
A: [...new Set(images.map(img => img.A))].sort((a, b) => a - b),
omega: [...new Set(images.map(img => img.omega))].sort((a, b) => a - b),
l: [...new Set(images.map(img => img.l))].sort((a, b) => a - b),
theta_0: [...new Set(images.map(img => img.theta_0))].sort((a, b) => a - b),
};
// Initialize current values to the minimums
const currentValues = {
A: uniqueValues.A[0],
omega: uniqueValues.omega[0],
l: uniqueValues.l[0],
theta_0: uniqueValues.theta_0[0],
};
// Initialize sliders
function initSliders() {
for (const param in uniqueValues) {
const slider = document.getElementById(`${param}-slider`);
const values = uniqueValues[param];
slider.min = 0;
slider.max = values.length - 1;
slider.value = values.indexOf(currentValues[param]);
}
}
// Update displayed image
function updateImage() {
const matchingImage = images.find(img =>
Math.abs(img.A - currentValues.A) < 0.01 &&
Math.abs(img.omega - currentValues.omega) < 0.01 &&
Math.abs(img.l - currentValues.l) < 0.01 &&
Math.abs(img.theta_0 - currentValues.theta_0) < 0.01
);
const imageElement = document.getElementById("simulation-image");
if (matchingImage) {
imageElement.src = matchingImage.file;
imageElement.alt = `Simulation Image: A=${matchingImage.A}, omega=${matchingImage.omega}, l=${matchingImage.l}, theta_0=${matchingImage.theta_0}`;
} else {
imageElement.src = "";
imageElement.alt = "No matching image found";
}
// Update displayed parameter values
document.getElementById("A-value").textContent = currentValues.A.toFixed(2);
document.getElementById("omega-value").textContent = currentValues.omega.toFixed(2);
document.getElementById("l-value").textContent = currentValues.l.toFixed(2);
document.getElementById("theta_0-value").textContent = currentValues.theta_0.toFixed(2);
}
// Change value for a parameter
function changeValue(param, direction) {
const values = uniqueValues[param];
const currentIndex = values.indexOf(currentValues[param]);
let newIndex = currentIndex + direction;
// Wrap around to the opposite end
if (newIndex < 0) {
newIndex = values.length - 1; // Go to max
} else if (newIndex >= values.length) {
newIndex = 0; // Go to min
}
currentValues[param] = values[newIndex];
document.getElementById(`${param}-slider`).value = newIndex; // Update slider value
updateImage(); // Update image and UI
}
// Update parameter value from slider
function updateSliderValue(param, sliderIndex) {
const values = uniqueValues[param];
currentValues[param] = values[sliderIndex];
updateImage();
}
// Initialize display
initSliders();
updateImage();
</script>
</body>
</html>