Lagrangian vs Hamiltonian Mechanics

Comments · 282

• AB

  @AbideByReason · 1 year ago · pinned

  To learn for free on Brilliant, go to <a href="https://brilliant.org/AbideByReason/">https://brilliant.org/AbideByReason/</a> . You’ll also get 20% off an annual premium subscription.

  15

• MI

  @midwittcuckoo · 1 year ago

  The Royal Society fielded a committee to decide whether Newton or Leibniz first discovered calculus. They decided in favour of Newton, who chaired the committee.

  775

• DR

  @drplasma1990 · 11 months ago

  During your degree of physics, you start with Lagrangian mechanics and you are scared. And then you learn them and you never want to go back to Newton&apos;s.

  243

• RA

  @raphaelreichmannrolim25 · 11 months ago (edited)

  The most general formulation of the Hamiltonian doesn&apos;t come from the Lagrangian. Mathematician Maria Lewtchuk Espíndola showed the existence of the DIRECT hamiltonization. It addresses the exact issue of a priori definitions of momenta! Search for her articles! The Legendre transform can only applied in the non linear case

  26

• OH

  @OhpleaseGodwakeMe · 1 year ago

  Simply beautiful. I use applied physics in my job, and I was modeling a very related phenomenon a while back at work, and pondering over the analytical solution for the oscillation. This video couldn&apos;t have come to me at a better time! Thank you!

  92

• VV

  @vv_vv7992 · 11 months ago

  Beautiful! Im an economist and I have to say Im feeling some “physics envy” for being able to encode first principles into these amazing alternative and equivalent perspectives

  11

• DO

  @doctor_smaug · 11 months ago

  Lagrange and Hamilton walk into a bar.<br><br>Lagrange says, “I’ll have a smooth drink that minimizes my discomfort.”<br>Hamilton says, “I’ll take the same — but expressed in canonical coordinates.”<br><br>The bartender blinks and mutters, “You two are just different formulations of the same problem, aren’t you?”<br><br>Lagrange grins, “Exactly.”<br>Hamilton nods, “But mine has better symmetry.”

  59

• NO

  @normanstewart7130 · 1 year ago

  <a href="https://www.youtube.com/watch?v=tpp1Ahmij_Q&amp;t=122">2:02</a> I met Cornelius Lanczos in 1973-74. He gave a talk at the Dublin University Experimental Science Association. Although he looked beatific, somewhat like Einstein, he was very pragmatic and worldly wise; he was there to promote his book! (The Einstein Decade). I&apos;d say he was a tough character; I wouldn&apos;t have liked to get into an argument with him!

  7

• US

  @user-pk5rc4or2w · 6 months ago (edited)

  Muy bueno. Me suscribo. &nbsp;Tengo 61, estudié Física en los 80&apos;s y ya estoy jubilado, tengo tiempo para ver estos interesantes vídeos. Saludos desde España.

  5

• AN

  @anandbavkar8572 · 1 year ago (edited)

  As someone who is self-studying, I can&apos;t thank you enough for these videos. They&apos;ve been a game-changer for me, finally making sense of concepts I&apos;ve always struggled with. Please keep up the fantastic work! Especially, First time understood &quot;Legendre Transformation&quot;. It would be nice if there is separate long video on &quot;Legendre Transformation&quot;. Thanks a Lot!!

  24

• US

  @user-ky6vw5up9m · 4 months ago

  Hamilton’s equations are cast into a stone bridge in Dublin. 16th October every year the mathematicians walk along the canal and gather at the bridge where Hamiltonian it is said had his flash of inspiration.

  2

• DO

  @douglasstrother6584 · 9 months ago

  Learning about non-linear oscillators, chaos and all that in Junior-level Classical Mechanics course put the &quot;WOW!&quot; back into Physics for me. &nbsp;Thanks, Professor Peter Scott (1933-2024), UC Santa Cruz (1983)! &nbsp;We studied the Düffing Oscillator and he had a real demo of it as well. &nbsp;The Logistic Map was another goodie he encouraged us to play with on a computer. <br>We covered perturbation theory in the context of non-linear oscillators and the 3-body central force problem; &nbsp;it&apos;s fascinating how complexity arises when you &quot;tweak things just a bit&quot;. <br> <br>Physics Honchos like Poincaré worked on non-linear mechanics in the early 1900&apos;s; &nbsp;he and others showed that &quot;these are <b>really</b> hard problems&quot;. &nbsp;Little more was done up to Edward Lorenz&apos;s modeling of weather in 1963, with the arrival of digital computers. <br>Non-linear systems are covered in &quot;Nonlinear Oscillations&quot; Ch.5 of &quot;Classical Dynamics&quot; (2nd ed.) by Jerry Marion, and in &quot;Canonical Perturbation Theory&quot; Ch.11 of &quot;Classical Mechanics&quot; (2nd ed.) by Herbert Goldstein. <br> <br>&quot;Chaos: Making a New Science&quot; by James Gleick is still a great read. <br> <br>There <b>is</b> more to life than boundary value problems!

  3