#lagrange — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #lagrange, aggregated by home.social.
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From #DEVONthink To Go’s update notice today:
"We’re naming this release after the mathematician Joseph-Louis #Lagrange (1736-1813) who made significant contributions to the fields of #analysis, #NumberTheory, and both classical and celestial #mechanics. Lagrange’s work has had a profound impact on our understanding of #celestial mechanics and has practical applications in #SpaceExploration."
That is exactly the kind of detail that makes me love this tool ❤️
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I’m tinkering with #geminiprotocol. I’ve installed #Amfora so I can use sites that require identity certs. The whole trust first on use (tofu) is batshit (says the idiot who always blindly trusts ssh host verification), but it’s kinda neat. #lagrange definitely has the whole ergonomics of identity certs lock down not a whiff of openssl command line magicks. Would’ve preferred to stick with bombadillo (it’s suports #GopherProtocol and #fingerprotocol), but can’t do certs). I would love to see a tui that can renders images using #sixel
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Anoche me adentré en el mundo texto-plano, finger , gopher , gemini, y cli; me parece que me he perdido y creo me será difícil volver al mundo tal y cual lo conocía, queeee hermosura!!! , todo conocimiento, sin distracción y con muchas cosas útiles. A propósito, usen Lagrange en el celular, precioso desde donde se lo vea. Dejo una imagen a modo de muestra.
#textoplano #textoplanoxyz #lagrange #gopher #gemini -
A cycloidal pendulum - one suspended from the cusp of an inverted cycloid - is isochronous, meaning its period is constant regardless of the amplitude of the swing. Please find the proof using energy methods: Lagrange's equations (in the images attached to the reply).
Background:
The standard pendulum period of \(2\pi\sqrt{L/g}\) or frequency \(\sqrt{g/L}\) holds only for small oscillations. The frequency becomes smaller as the amplitude grows. If you want to build a pendulum whose frequency is independent of the amplitude, you should hang it from the cusp of a cycloid of a certain size, as shown in the gif. As the string wraps partially around the cycloid, the effect decreases the length of the string in the air, increasing the frequency back up to a constant value.In more detail:
A cycloid is the path taken by a point on the rim of a rolling wheel. The upside-down cycloid in the gif can be parameterized by \((x, y)=R(\theta-\sin\theta, -1+\cos\theta)\), where \(\theta=0\) corresponds to the cusp. Consider a pendulum of length \(L=4R\) hanging from the cusp, and let \(\alpha\) be the angle the string makes with the vertical, as shown (in the proof).#Pendulum #Cycloid #Period #Frequency #SHM #TimePeriod #CycloidalPendulum #Lagrange #Cusp #Energy #KineticEnergy #PotentialEnergy #Lagrangian #Length #Math #Maths #Physics #Mechanics #ClassicalMechanics #Amplitude #CircularFrequency #Motion #Vibration #HarmonicMotion #Parameter #ParemeterizedEquation #GoverningEquations #Equation #Equations #DifferentialEquations #Calculus
