Buy me a coffee and support the channel: In this video, I present an overview of symmetries in physics, passive vs. active transformations, and how to derive Noether's theorem from the Euler-Lagrange equations. Different examples are presented in detail to show how the invariance under specific symmetries can be used to construct conserved quantities. [Related videos] ∘ Lagrangian Mechanics: when theoretical physics got real [References] ∘ C. Huygens, "A summary account of the laws of motion," Philos. Trans. R. Soc. 4, 925 (1669) ∘ G. E. Smith, "The vis viva dispute: A controversy at the dawn of dynamics," Physics Today Oct. (2006) ∘ E. Noether, "Invariante Variationsprobleme," Nachr. v. d. Ges. d. Wiss. zu Göttingen, 235 (1918) [Credits] Sunflower by M. Mingle, public domain Newton's cradle by Thirdman, free use via Pexels Emmy Noether, public domain Faucault's pendulum by M. Espejo, free use via Pexels Curling stones by SHVETS production, free use via Pexels LHC collision by CERN in "CERN: 50 years of Science" Cassini spacecraft by NASA in JPL and the Space Age: Triumph at Saturn Galileo Galilei's "Dialogo" by Nightryder84 under CC BY-SA 3.0 Portrait of René Descartes by Frans Hals, public domain Christiaan Huygens, the astronomer, public domain Rolling sphered fruits by M. Leonova, free use via Pexels Philosophiae Naturalis Principia Mathematica by P. Hermans under CC BY-SA 3.0 Lagrange's Analytical Mechanics, public domain Albert Einstein, public domain Einstein's Zurich Notebook, public domain David Hilbert, public domain Felix Klein, public domain Paul Albert Gordan, public domain Clebsch-Gordan coefficients by Particle Data Group Emmy Noether's paper via European Digital Mathematics Library Snowflake by J. Lass under CC BY 4.0 Camera in a stabilizer by A. Preciado, free use via Pexels Woman taking photos by A. Sandrini, free use via Pexels Kittens learn Newton's cradle by Funny Cats and Nice Fish under CC BY 3.0 CC BY 3.0 CC BY-SA 3.0: CC BY 4.0: