The origin of Hamiltonian Mechanics

Buy me a coffee and support the channel: https://ko-fi.com/jkzero In this video, I present one of the most influential formulations of classical physics — Hamiltonian mechanics. This is a walk through the birth of Hamiltonian mechanics and how Hamilton extended Lagrange’s work into a new, elegant formulation that would go on to influence quantum theory, statistical mechanics, and dynamical systems. [Related videos] ∘ Symmetry in physics and Noether’s theorem    • Symmetry in physics and Noether’s theorem   ∘ Lagrangian Mechanics: when theoretical physics got real    • Lagrangian Mechanics: when theoretical phy...   ∘ Legendre Transform by Abide By Reason    • A Simple yet Powerful Math Trick   ∘ Leonard Susskind: interview by Udemy    • Leonard Susskind - The Best Differential E...   [References] ∘ A-M. Legendre, "Mémoire sur l'intégration de quelques équations aux différences partielles," Histoire de l'Académie royale des sciences 309 (1787) ∘ W. R. Hamilton, "Second Essay on a general method in dynamics," Phil. Trans. R. Soc.125, 95 (1835) https://doi.org/10.1098/rstl.1835.0009 ∘ W. Heisenberg, "Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen," Z. Phys. 33, 879 (1925) ∘ M. Born and P. Jordan, "Zur Quantenmechanik,” Z. Phys. 34, 858 (1925) ∘ Euler's homogeneous function theorem (Wikipedia) https://en.wikipedia.org/wiki/Homogen... [Credits] Philosophiae Naturalis Principia Mathematica by P. Hermans under CC BY-SA 3.0 Portrait of Adrien-Marie Legendre, public domain Joseph Louis Lagrange, public domain Lagrange's Analytical Mechanics, public domain William Rowan Hamilton, public domain A-M. Legendre, public domain Werner Heisenberg by AIP Max Born by AIP Pascual Jordan by AIP Force diagrams by W.J.'s Gravesande, public domain Mathematical elements of natural philosophy, confirm'd by experiments Phase space of a simple pendulum by J. Bertolotti, public domain Phase space of a double pendulum by J. Bertolotti, public domain AIP: American Institute of Physics, Emilio Segrè Visual Archives CC BY-SA 3.0: https://creativecommons.org/licenses/...