Небесная механика, или Удивительная геометрия фейерверка

In this video, we'll discuss firework geometry, as well as ballistics, celestial mechanics, Kepler's laws, and a problem that gave Newton a headache. Animations created using Manim:    • Как создавать математические анимации?   Support the channel: https://boosty.to/wildmathing SOURCES 1) Zaslavsky, A. A., Nilov, F. K., "Firework Geometry," Quantum. 2023, no. 1, pp. 39–41: https://www.kvant.digital/issues/2023... 2) Henri Poincaré. New Methods of Celestial Mechanics 3) Celestial Mechanics Course by Alexander Chirtsov: https://www.lektorium.tv/skymechanics 4) Astronomy Course by Vladimir Surdin: https://www.lektorium.tv/astronomy SOCIAL MEDIA Telegram: https://t.me/wildmathing TikTok:   / wildmathin   Boosty: https://boosty.to/wildmathing VK: https://vk.com/wildmathing For Teachers: https://vk.com/wm_teachers For Applicants: https://vk.com/wm_students CONTENTS 0:00 — What is the video about? 0:30 — Parabolic Fireworks 1:14 — Ballistic Experiments 2:15 — Newton's Thought Experiment 3:00 — From Copernicus to Kepler 3:55 — Geometric Definition of an Ellipse 4:15 — Kepler's First Law 4:45 — Kepler's Second Law 5:35 — Kepler's Third Law 6:05 — What Did Newton Do? 6:43 — Newton's Headache 7:37 — Chaos in the Three-Body Problem 8:19 — Conquering Space 8:45 — Geometric Definition of a Parabola 9:07 — The Beautiful Properties of Parabolic Fireworks 9:52 — Elliptical Fireworks 11:40 — Experiments with Initial Velocity 12:20 — Three-Dimensional Theorems 12:46 — Particle Front of an Elliptical Fireworks 13:30 — What Causes Gravity? 2:06 PM — On Visual Simplifications 2:45 PM — Acknowledgments MUSIC LICENSES PVQ5HSXQJLDZWFVL ZYXSSOTWYL1FVU7B H2EJT6YHN30MP8QY 6J5IN6JBCKZG9BEL XIXU6NDBX2NDUKVD MPQZL3YN1U2YL8TN CNJNALB0LKQESI2F IMVAESWRMCELHXLN This video uses Johann Strauss's composition from the symphonic poem "Thus Spoke Zarathustra" under a Creative Commons license:    • Also Sprach Zarathustra - Strauss [COPYRIG...   Recording: "Lud and Schlatts Musical Emporium"