{"product_id":"double-pendulum-chaotic-motion-demonstration","title":"Double Pendulum — Chaotic Motion Demonstration","description":"\u003cp\u003eTwo pendulums linked at a joint. Perfectly deterministic equations of motion. Completely unpredictable behaviour. This is chaos theory made physical.\u003c\/p\u003e\u003cp\u003eThe double pendulum is the canonical example of deterministic chaos. Its equations are derived from Newtonian mechanics with no approximations — and yet it is exquisitely sensitive to initial conditions. Start it from nearly the same position twice and the trajectories diverge exponentially. The tiniest quantum fluctuation matters. It is why long-term weather forecasting is impossible in principle, not just in practice.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eWhat you can demonstrate:\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eSensitive dependence on initial conditions\u003c\/li\u003e\n\u003cli\u003eLyapunov exponents and the butterfly effect\u003c\/li\u003e\n\u003cli\u003eThe difference between determinism and predictability\u003c\/li\u003e\n\u003cli\u003eLagrangian mechanics and generalized coordinates\u003c\/li\u003e\n\u003cli\u003ePhase space and strange attractors\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\u003cstrong\u003eSpecifications:\u003c\/strong\u003e Polished stainless steel arms · Low-friction precision bearings · Magnetic base · Optional LED trace attachment sold separately · Height: 40cm\u003c\/p\u003e\u003cp\u003eHypnotic to watch. Impossible to predict. Entirely explained by F = ma.\u003c\/p\u003e","brand":"Golden Physics Project","offers":[{"title":"Default Title","offer_id":54140237349156,"sku":"GPP-DOUBLE-PENDULUM","price":64.99,"currency_code":"CAD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1007\/2879\/9524\/files\/Sc3f6e0f6390e48188ec5e8ed573591fdN.jpg_480x480q75.webp?v=1780994233","url":"https:\/\/shop.goldenphysics.org\/products\/double-pendulum-chaotic-motion-demonstration","provider":"Golden Physics Project","version":"1.0","type":"link"}