A few days back, I posted some #AnimatedGifs of the exact solution for a large-amplitude undamped, unforced #Pendulum. I then thought to complete the study to include the case when it has been fed enough #energy to allow it just to undergo #FullRotations, rather than just #oscillations. Well, it turns out that it is “a bit more complicated than I first expected” but I finally managed it.
#Mathematics #AppliedMathematics #SpecialFunctions #DynamicalSystems #NonlinearPhenomena
Here we see three identical pendulums, oscillating independently. The red and purple ones are vibrating with small amplitudes and so their periods are nearly the same. But the blue one is undergoing what would be considered to be very large amplitude oscillations and has a significantly longer period. In fact, as the amplitude approaches π radians, the period increases without bound and approaches infinity.
#MyWork #CCBYSA #Mathematics #ClassicalMechanics #AppliedMathematics #Physics #Animation
The above is only strictly true for “small” amplitudes. If the #pendulum is subject to large amplitudes, it is no longer governed by the simple linear differential equations alluded to above. Given that the rod remains rigid and no energy is dissipated, the pendulum #equations may still be solved exactly, though they are now #nonlinear.
#MyWork #CCBYSA #Mathematics #ClassicalMechanics #AppliedMathematics #Physics #Animation
In elementary #mechanics we are taught about the #SimplePendulum, which is modelled as a point #mass hanging via a rigid #rod or #string of a given length, under uniform #gravity. This simple model is also useful in introducing #OrdinaryDifferentialEquations and helps us to understand #SimpleHarmonicMotion.
#MyWork #CCBYSA #Mathematics #ClassicalMechanics #AppliedMathematics #Physics #Animation
Job Alert 🌱
🎓 Tandem Professur (W1 LBesO) Sichere Software Systeme
Deadline: 2025-05-26
Location: Germany, Zweibrücken, Rheinland Pfalz
🔗 https://www.academiceurope.com/job/?id=7612
#hiring #Professor #ITSecurity #SoftwareEngineering #AI #TandemProfessur #informatics #appliedphysics #appliedmathematics
Whoa, after more than a year of work (the last 2 months were quite brutal), I submitted my (applied math) Master's thesis 'Computational analysis in neuroscience':
Job - Alert 🌱
🌎 #PhD Position (f_m_x) – Uncertainty Analysis of Coupled Reactive Transport Models
Deadline: 2025-05-27
Location: Germany, Potsdam, Brandenburg
https://www.academiceurope.com/job/?id=7517 🌎
#hiring #AppliedMathematics #ComputerSciences #geochemistry #GeoScience #Programming #Statistics
"The "Correlation" Between Statistics and Eugenics" (2024) 2/2
https://lareviewofbooks.org/article/the-correlation-between-statistics-and-eugenics/
#statistics
#philosophy
#philosophyofscience
#mathematics
#appliedmathematics
#eugenics
@philosophy@a.gup.pe
@philosophy
I cannot think of an applied mathematics that is more beautiful and far-reaching, or philosophically wilder, than probability. No, nonlinear dynamics and chaos people, it’s not even close 🤣
#probability
#mathematics
#appliedmathematics
#philosophy
#philosophyofscience
@philosophy
@philosophy@a.gup.pe
We’re having a #Soliton sale over here! Get yours quick! Seriously, though, this is a quick #animation of the #SolitonInteraction surface – the solution of the #Korteweg-deVries #Eauation showing (x,t,u(x,t)) giving you an all-round view.
#MyWork #CCBYSA #AppliedMathematics #Mathematic #Phyiscs #KdV #KdVEquation #FreeSoftware #WxMaxima
Khurram Wadee ✅
Academic Europe
sceptri
david jon furbish