In this video, I solve the nonlinear dynamics problem of the pendulum without using the small angle approximation. The final result involves elliptic integral functions and beta functions.

Intro: (00:00)
First integral of motion: (00:40)
Consequences: (10:06)
General solution: (13:40)
Time period: (21:00)
Small angle limit: (29:20)

#physics #pendulum #smallangle #mechanics #mathematics #calculus #trigonometry #analysis #sum #integral #integralcalculus #sines #cosine #differentialequation #nonlinear #gravity #beta #gamma #taylorseries #asymptotic

#drpeyam #blackpenredpen #flammablemaths #3blue1brown #michaelpenn #khanacademy #tibees #andrewdotson #stevemould #vibingmaths