Nikita Lisitsa
@lisyarus.bsky.social did:plc:3akwoh4ywphuebl6zalsdif5
He/him I teach C++ & computer graphics and make videogames Working on a medieval village building game: https://youtube.com/playlist?list=PLSGI94QoFYJwGaieAkqw5_qfoupdppxHN&cbrd=1 Check out my cozy road building traffic sim: https://t.ly/FfOwR
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Nikita Lisitsa (@lisyarus.bsky.social) é um usuário do Bluesky desde 24 outubro 2023. Tem 7.898 seguidores, segue 981 contas e publicou 3.124 posts.
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Sounds like I am way too academic and favour generalized tools 🤭 In particular cases as in your post maybe it's significantly better to switch to shorter solution, though.
Ver postThe functional in your post doesn't depend on derivatives but the E-L equations are still doing their job nicely. It's just like using the 2nd Law of Newton when yor are solving the problem on dynamics you almost always use it.
Ver postI treat them in general manner, i.e. equations on functions and not variables. As far as I remember in theoretical mechanics where the functions of one variable are studied they are called Lagrange equations. In variational calculus they are called Euler equations. Hence the general name (E-L).
Ver postSleepy beanie day 🍁
Ver postYep, but one needs to know that they exist. And you used the series to find the solution. So basically you followed along the path how these equations are derived. From pedagogical viewpoint I suppose that's a much better way because one doesn't need to know what calculus of variations is about!
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