Euler Lagrange Equations
Hamiltons Principle ⇒ Minimizing S[L]
Minimizing S[L] ⇒ Solving E.L Equations for 𝐱(𝑡)
E.L Equations replaces 𝐅=𝑚𝐚pic.twitter.com/tU9ZTvxRcf
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Hamiltons Principle
HP states that the path a particle takes between two points is the one that minimizes the action S[L]
L is called the Lagrangian: it is the difference between kinetic and potential energy
HP is equivalent to Newton's laws of motionpic.twitter.com/vCL6sw6zLj
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Example: Consider a particle of mass 𝑚 subject only to gravity.
Solving the E.L equations gives precisely what we would have obtained from Newton's lawspic.twitter.com/YUB8lmByNX
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You are a natural teacher. I hope you are a professor someday.
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Thanks friend! Means a lot
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Worth to mention also: Maupertius principle (least length); Huygens-Fresnel principle; Fermat's principle (least time, mathematical realization of Huygens-Fresnel principle). Rayleigh-Ritz VP And my favorite: The Einstein-Hilbert Action (with the Palatini identity);-)
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My second choice: The simplified expression for the Lagrangian of the Standard Model on a mug: The original Lagrangian is much more complicated and the MSSM Lagrangian more elegant. The SU(5) -although not realistic- is my 3rd favorite ;-)pic.twitter.com/eh5DCEDAKQ
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