#lagrangian — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #lagrangian, aggregated by home.social.
-
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
-
An aerospace engineering student from the Pennsylvania State University refines a 100-year-old math/aerodynamic (wind energy equation) problem, expanding wind energy possibilities.
Article published in Wind Energy Science:
https://wes.copernicus.org/articles/10/451/2025/Read more:
[1] https://timesofindia.indiatimes.com/education/news/meet-divya-tyagi-the-penn-state-student-who-cracked-a-100-year-old-wind-energy-equation-boosting-turbine-efficiency/articleshow/119260883.cms
[2] https://www.psu.edu/news/engineering/story/student-refines-100-year-old-math-problem-expanding-wind-energy-possibilities#Aerospace #Science #Math #Maths #Aerodynamics #Wind #WindEnergy #Equation #Lagrangian #Aerodynamic #WES #Turbine #Turbines #Efficiency #Energy #Divya #DivyaTyagi #Tyagi #Penn #PSU #PennState #AerospaceEngineering #Engineering
-
Tracking Ice Floes
To understand why some sea ice melts and other sea ice survives, researchers tracked millions of floes over decades. This herculean undertaking combined satellite data, weather reports, and buoy data into a database covering nearly 20 years of data. With all of that information, the team could track the changes to specific pieces of ice rather than lumping data into overall averages.
They found that an ice floe’s fate depended strongly on the route it took: ice that slipped from its starting region into warmer, more southern regions was likely to melt. They also saw region-specific effects, like that thick sea ice was more likely to melt in the East Siberian Sea’s summer, possibly due to warmer currents. The comprehensive, fine-grained analyses possible with this ice-tracking technique offer a chance to understand why some Arctic regions are more vulnerable to warming than others. (Image credit: D. Cantelli; research credit: P. Taylor et al.; via Eos)
#climateChange #Eulerian #fluidDynamics #Lagrangian #melting #physics #planetaryScience #science #seaIce
-
New #python #physics video - building a 3D animation of a half-atwood with a spring using #Lagrangian mechanics and #sympy (of course #vpython too)
-
New #physics #lagrangian - flinging a bead from a rotating stick. Yes, of course there is a #python model. Do you not even know me?
-
New #physics #classicalmechanics video - a mass slides down a frictionless parabola. Will it ever lose contact with the surface? Solved using #lagrangian and #python
-
New #physics video - using Lagrange Multipliers to find forces of constraint.
#classicalmechanics #lagrangian -
New #physics #lagrangian video - a chain sliding off a table (yes, animated in #webvpython of course)
-
There are just too many #lagrangian #physics problems - but I had to do a bead on a rotating hoop. Of course #python is included.
-
Yes. I have ANOTHER #Lagrangian mechanics problem for you - a pendulum on an oscillating pivot point. #physics. #python
https://youtu.be/ITlSFagJPAo -
New #physics video - my introduction to #Lagrangian mechanics
-
If intro physics were taught in a modern way, this is how it would look, with action principles. Veritasium’s new video is excellent. #ITeachPhysics #Action #Lagrangian #EulerLagrange
-
Everything is an intersection of #Lagrangian #submanifolds, implying fundamental #locality. The apparent non-localities in #QuantumMechanics, arising from #measurement #incompatibility, suggest that at a deeper level, quantum mechanics is equivalent to classical #ergodic systems.
-
Everything is an intersection of #Lagrangian #submanifolds, implying fundamental #locality. The apparent non-localities in #QuantumMechanics, arising from #measurement #incompatibility, suggest that at a deeper level, quantum mechanics is equivalent to classical #ergodic systems.
-
Everything is an intersection of #Lagrangian #submanifolds, implying fundamental #locality. The apparent non-localities in #QuantumMechanics, arising from #measurement #incompatibility, suggest that at a deeper level, quantum mechanics is equivalent to classical #ergodic systems.
-
Question: What is the derivative of the Lagrangian (of what system I don't particularly care right now) with respect to entropy (or to the time derivative of entropy)? Is this even a sensible question? Can we use the Euler-Lagrange equation for entropy?
#lagrangian #lagrangianMechanics #physics #physicsQuestion #entropy #eulerLagrangeEquation #eulerLagrangeEquations
-
Congratulations to dr (*) Jacob Richardson, who successfully (*) defended his PhD thesis "On Discrete Lagrangian Multiform Structures and their Reductions" in the face of persistent questioning from Andy Hone and myself.
Well done to his supervisors Frank Nijhoff and Vincent Caudrelier. Some results are described in the preprint of Jacob and @mathmats, "Discrete Lagrangian multiforms for quad equations, tetrahedron equations, and octahedron equations", https://arxiv.org/abs/2403.16845 .
(*) subject to editorial and presentational corrections
-
I saw this interesting #physics question with 4 masses and springs on @aapt communities - and I just HAD to solve it THREE different ways (#lagrangian and #python included)
-
How the #Higgs Mechanism Gives Things #Mass
https://www.youtube.com/watch?v=G0Q4UAiKacw&ab_channel=PBSSpaceTime
#PBS #SpaceTime #PBSSpaceTime #HiggsBoson #Boson #HiggsMechanism #HiggsField #Symmetry #U1 #SU2 #BrokenSymmetry #GaugeField #GaugeBoson #GoldstoneBoson #QM #QuantumMechanics #QuantumPhysics #Phase #Lagrangian #MattODowd
-
Very cool that some of our #Ukraine partners in @PolarRES have made it to Utrecht in person to present some of their results on #Lagrangian #ParticleTracking under the Ross and Filchner-Ronne #IceShelves as part of the #PolarRES + #PolarCORDEX meeting
Edit to add link to paper:
-
Provably Convergent Policy Optimization via Metric-aware Trust Region Methods
Jun Song, Niao He, Lijun Ding, Chaoyue Zhao
Action editor: Amir-massoud Farahmand.
-
Will a block sliding down a parabola lose contact? Here is my #lagrangian constraint video
-
The #Equation That Explains (Nearly) Everything.
https://www.youtube.com/watch?v=PHiyQID7SBs&ab_channel=PBSSpaceTime
#Science #Physics #Lagrangian #Lagrangians #StandardModel #StandardModelLagrangian #SML #Cosmology
#PBS #PBSSpaceTime #SpaceTime #MattODowd -
New #physics video from my #classicalMechanics series on #Lagrangian - a half swinging atwood machine
-
The #Equation That Explains (Nearly) Everything!
https://www.youtube.com/watch?v=PHiyQID7SBs
#StandardModel #Physics #Science #Equations #PBS #PBSSpacetime #Spacetime #Lagrangian #StandardModelLagrangian