# Christiaan Huygens
## Microsim
### Live player
<div class="microsim-player">
<iframe src="https://editor.p5js.org/sciencenibber/full/cGN9kEQ9A" width="100%" height="620" frameborder="0" sandbox="allow-scripts allow-same-origin"></iframe>
</div>
<div class="microsim-fallback">
<img src="Microsims/thumbs/Christiaan_Huygens.png" alt="Christiaan_Huygens microsim poster" style="width:100%;border:1px solid #4445;border-radius:6px;">
<p><em>Live microsim (desktop) · <a href="https://editor.p5js.org/sciencenibber/sketches/cGN9kEQ9A">open sketch in the p5.js editor</a></em></p>
</div>
**Editor URL:** https://editor.p5js.org/sciencenibber/sketches/cGN9kEQ9A
**Description (100 words):**
A simple pendulum swings under exact (nonlinear) physics while the sketch tracks where its energy lives. Christiaan Huygens built the first pendulum clock in 1657 and derived the small-amplitude period T = 2*pi*sqrt(L/g), shown live in the readout. As the bob falls toward the bottom of its arc it trades potential energy for kinetic energy, then climbs and trades it back; the stacked bar on the right shows kinetic (blue) and potential (orange) energy swapping while their sum, the total mechanical energy E, stays flat. Drag the length L, release angle theta0, and gravity g to see motion and period respond.
```js
// =====================================================================
// Article : Christiaan Huygens
// Slug : Christiaan_Huygens
// Wikitube : en.wikitube.io/wiki/Christiaan_Huygens
// Room : Energy
//
// Idea : Huygens (1629-1695) invented the pendulum clock (1657) and
// was first to derive the small-amplitude period of a simple
// pendulum, T = 2*pi*sqrt(L/g). This microsim swings a simple
// pendulum under exact (nonlinear) physics and shows the
// continuous exchange between kinetic and potential energy:
// the bob trades height for speed, but the TOTAL mechanical
// energy E = KE + PE stays flat. Adjust the length L, the
// release angle theta0, and gravity g, and watch both the
// motion and the predicted period respond.
//
// Equation : T = 2*pi*sqrt(L/g) (small-angle period)
// E = KE + PE = (1/2) m L^2 w^2 + m g L (1 - cos theta)
// =====================================================================
// Rule 3 - single source of truth for the title/URL/save-name.
const ARTICLE = "Christiaan_Huygens";
// Rule 4 - disable the Friendly Error System for ship.
p5.disableFriendlyErrors = true;
// ---------- controls ----------
let lenSlider; // L pendulum length (metres)
let angSlider; // theta0 release angle (degrees)
let gSlider; // g gravitational acceleration (m/s^2)
let resetBtn; // re-release from theta0 with zero velocity
// ---------- dynamical state ----------
let theta; // current angular displacement (radians)
let omega; // current angular velocity (rad/s)
const M = 1; // bob mass (kg) - cancels in the motion, kept for energy
let dtScale = 2.5; // wall-clock -> sim-time multiplier (visual pacing)
// ---------- layout constants (computed in setup) ----------
let pivotX, pivotY; // pendulum suspension point on canvas
let pxPerMetre; // pixels used to draw one metre of string
function setup() {
// Rule 5 - canvas inside setup, standard size, retina density.
createCanvas(720, 520);
pixelDensity(2);
// Suspension point sits high and centre-left of the swing area.
pivotX = width * 0.42;
pivotY = 96;
pxPerMetre = 150; // a 1 m string draws as 150 px
// Rule 6 - controls built in setup, positioned explicitly, in a
// dedicated bottom strip that the HUD layout leaves clear.
lenSlider = createSlider(0.4, 2.0, 1.0, 0.05); // L in metres
lenSlider.position(150, height - 86);
lenSlider.style("width", "200px");
angSlider = createSlider(5, 80, 35, 1); // theta0 in degrees
angSlider.position(150, height - 60);
angSlider.style("width", "200px");
angSlider.input(release); // re-release whenever the amplitude changes
gSlider = createSlider(1.6, 24.8, 9.8, 0.1); // g in m/s^2
gSlider.position(150, height - 34);
gSlider.style("width", "200px");
resetBtn = createButton("release");
resetBtn.position(370, height - 60);
resetBtn.mousePressed(release);
release(); // set initial theta/omega from the slider amplitude
}
// Re-release the bob: start at the slider amplitude, at rest.
function release() {
theta = radians(angSlider.value());
omega = 0;
}
function draw() {
background(248);
// ---------- read controls ----------
const L = lenSlider.value();
const theta0 = radians(angSlider.value());
const g = gSlider.value();
// ---------- physics: exact (nonlinear) simple pendulum ----------
// theta'' = -(g/L) sin(theta). Integrate with a few small semi-implicit
// Euler substeps per frame for energy-stable motion at any amplitude.
const steps = 8;
// Clamp the frame's sim-time advance: the first frame (and any lag
// spike) reports a huge deltaTime, and a single large Euler step would
// inject energy and blow the swing up. Cap at 33 ms of sim time/frame.
const frameDt = Math.min((deltaTime / 1000) * dtScale, 0.033);
const dt = frameDt / steps;
for (let i = 0; i < steps; i++) {
const alpha = -(g / L) * sin(theta); // angular acceleration
omega += alpha * dt; // semi-implicit: v first...
theta += omega * dt; // ...then x, conserves energy
}
// ---------- energies (m = 1) ----------
const KE = 0.5 * M * L * L * omega * omega; // (1/2) m L^2 w^2
const PE = M * g * L * (1 - cos(theta)); // m g L (1 - cos theta)
const E = KE + PE; // total (should be flat)
const Emax = M * g * L * (1 - cos(theta0)); // energy budget at release
const period = TWO_PI * sqrt(L / g); // Huygens' small-angle T
// ---------- bob position ----------
const bx = pivotX + L * pxPerMetre * sin(theta);
const by = pivotY + L * pxPerMetre * cos(theta);
// ---------- reference geometry (layer 1, neutral grey) ----------
// Vertical equilibrium line and the swing arc the bob traces.
stroke(210);
strokeWeight(1);
line(pivotX, pivotY, pivotX, pivotY + L * pxPerMetre + 10);
noFill();
arc(pivotX, pivotY, 2 * L * pxPerMetre, 2 * L * pxPerMetre,
HALF_PI - theta0, HALF_PI + theta0);
// ---------- active geometry (layer 2, accents) ----------
// String + bob in blue.
stroke(40, 90, 200);
strokeWeight(3);
line(pivotX, pivotY, bx, by);
fill(40, 90, 200);
noStroke();
circle(bx, by, 30);
// Pivot dot.
fill(60);
circle(pivotX, pivotY, 8);
// ---------- energy bars (right side) ----------
drawEnergyBars(KE, PE, Emax);
// ---------- HUD watermark (rule 2) ----------
noStroke();
textFont("system-ui");
// 2a - top-left title block.
fill(20);
textSize(20);
textAlign(LEFT, TOP);
text("Christiaan Huygens - the pendulum clock", 16, 14);
textSize(12);
fill(110);
text("Wikitube microsim - en.wikitube.io/wiki/" + ARTICLE, 16, 40);
// 2b - top-right control hints.
textAlign(RIGHT, TOP);
textSize(11);
fill(110);
text("sliders: L (length), theta0 (release angle), g (gravity)", width - 16, 14);
text("KE and PE trade off; total E stays constant", width - 16, 30);
// 2c - bottom-left live readouts in canonical symbols.
textAlign(LEFT, BOTTOM);
textSize(13);
fill(20);
text("T = " + period.toFixed(2) + " s", 16, height - 116);
fill(40, 90, 200);
text("KE = " + KE.toFixed(2) + " J", 16, height - 100);
fill(200, 120, 30);
text("PE = " + PE.toFixed(2) + " J", 130, height - 100);
fill(60);
text("E = " + E.toFixed(2) + " J", 250, height - 100);
// Slider labels (rule 7) - left of each slider, right-aligned.
textAlign(RIGHT, CENTER);
textSize(12);
fill(60);
text("L = " + L.toFixed(2) + " m", 144, height - 86 + 8);
text("theta0 = " + angSlider.value() + " deg", 144, height - 60 + 8);
text("g = " + g.toFixed(1), 144, height - 34 + 8);
// 2d - bottom-right equation footer (ASCII only).
textAlign(RIGHT, BOTTOM);
textSize(11);
fill(80);
text("T = 2*pi*sqrt(L/g) | E = (1/2) m L^2 w^2 + m g L (1 - cos theta)",
width - 16, height - 8);
}
// ---------- helpers ----------
// Draw stacked KE/PE bars against the energy budget Emax so the reader
// sees the two quantities swap while their sum (the bar height) holds.
function drawEnergyBars(KE, PE, Emax) {
const x = width - 70;
const w = 34;
const baseY = height - 150;
const h = 230;
const scale = Emax > 1e-9 ? h / Emax : 0;
// Frame and budget line.
noFill();
stroke(180);
strokeWeight(1);
rect(x, baseY - h, w, h);
// PE fills from the bottom (orange), KE stacks on top (blue).
const peH = PE * scale;
const keH = KE * scale;
noStroke();
fill(200, 120, 30);
rect(x, baseY - peH, w, peH);
fill(40, 90, 200);
rect(x, baseY - peH - keH, w, keH);
// Label.
fill(110);
textAlign(CENTER, TOP);
textSize(11);
text("E budget", x + w / 2, baseY + 6);
textAlign(CENTER, BOTTOM);
text("KE", x + w / 2, baseY - h - 6);
}
```
## Links (Wikipedia order)
<!-- injected from _registry/childlinks/Christiaan_Huygens.json (2026-07-30T02:09:12Z) -->
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## From the Real GENERATIVE library
*Christiaan Huygens — placed from the Real G.E.N.E.R.A.T.I.V.E. course library (Engineering room). Source: Wikimedia Commons (via Wikipedia article media). [Details & license](https://commons.wikimedia.org/wiki/File:Christiaan_Huygens-painting.jpeg).*
*Animated: Christiaan Huygens — placed from the Real G.E.N.E.R.A.T.I.V.E. course library (Engineering room). Source: Wikimedia Commons (via Wikipedia article media). [Details & license](https://commons.wikimedia.org/wiki/File:Collision_huygens.gif).*
> Christiaan Huygens, Lord of Zeelhem, FRS (/ˈhaɪɡənz/ HY-gənz,[2] .IPA-label-small{font-size:85%}.references .IPA-label-small,.infobox .IPA-label-small,.navbox .IPA-label-small{font-size:100%}US also /ˈhɔɪɡənz/ HOY-gənz;[3] Dutch: [ˈkrɪstijaːn ˈɦœyɣə(n)s] ⓘ; also spelled Huyghens; Latin: Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physic ([Wikipedia](https://en.wikipedia.org/wiki/Christiaan_Huygens))
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## From the vault media library
!Christiaan Huygens thumb.png
*Christiaan Huygens — from the vault's own media holdings, placed 2026-07-09. MTN / Wikitube.io original · CC BY-SA 4.0.*
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**Semiotic universals** (the notations and alphabet letters this article speaks — each opens its canonical card): ipa · kanji radicals · energy · amplitude · flow. Index: the glyph gallery · SEMIOTICS PORTAL.
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> **Room:** [[Energy]] · **Status:** ✅ shipped
## Overview
Christiaan Huygens, Lord of Zeelhem, FRS (/ˈhaɪɡənz/ HY-gənz,2 .mw-parser-output .IPA-label-small{font-size:85%}.mw-parser-output .references .IPA-label-small,.mw-parser-output .infobox .IPA-label-small,.mw-parser-output .navbox .IPA-label-small{font-size:100%}US also /ˈhɔɪɡənz/ HOY-gənz;3 Dutch: ˈkrɪstijaːn ˈɦœyɣə(n)s ⓘ; also spelled Huyghens; Latin: Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution.45 In [[Physics|physics]], Huygens made seminal contributions to optics and mechanics, while as an astronomer he studied the rings of Saturn and discovered its largest moon, Titan. As an engineer and inventor, he improved the design of telescopes and invented the [[Pendulum|pendulum]] clock, the most accurate timekeeper for almost 300 years. A talented mathematician and physicist, his works contain the first idealization of a physical problem b
_(Overview is shorter than 200 words; the pipeline should expand it from textbook context before publishing.)_
## See also
- Room hub: [[Energy]]
- p5.js Editor conventions: P5 JS EDITOR
- Wiki root: MAIN
---
*Scaffolded by `generative-microsim` from row 13 of the Energy sheet on 2026-06-03T15:48:18Z.*
Letters: energy · amplitude · ipa · flow · mined_geometry · mined_system · potential · conservation
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*Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*
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## Wikipedia : Wikitube
**Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Christiaan_Huygens) : [Wikitube](https://en.wikitube.io/wiki/Christiaan_Huygens)
## Previous hub tags
Tree parents: [[Decision_theory]] · [[Game_theory]] · [[Operations_research]].
Legacy hubs: `GENERATIVE`.
---
*Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*