Ideal Double Pendulum

Last updated on Aug 18, 2022

Rendered in Blender.

The double pendulum is tackled in every classical mechanics lecture and it is animated very often. In this project I wanted to make get acquainted with Blender. 3D animations are often not as meaningful scientifically as in 2D, but still very pretty. Always nice to look at for science communication as well. The simulation was done with Mathematica. Another interesting exercise would be the animation of the three-body problem!

\begin{aligned} {\ddot{θ}}_{1} & = - \frac{m_{2}}{m_{1} + m_{2}} \frac{l_{2}}{l_{1}} ({\ddot{θ}}_{2} \cos (θ_{1} - θ_{2}) + {\dot{θ}}_{2}^{2} \sin (θ_{1} - θ_{2})) - \frac{g}{l_{1}} \sin (θ_{1}) \\ {\ddot{θ}}_{2} & = - \frac{l_{1}}{l_{2}} ({\ddot{θ}}_{1} \cos (θ_{1} - θ_{2}) - {\dot{θ}}_{1}^{2} \sin (θ_{1} - θ_{2})) - \frac{g}{l_{2}} \sin (θ_{2}) \end{aligned}

Boundary conditions

$\begin{aligned} θ_{1} (0) & = \frac{π}{2} \\ θ_{2} (0) & = π \\ {\ddot{θ}}_{1} (0) & = 0 \\ {\ddot{θ}}_{2} (0) & = 0 \\ l_{1} & = 1 \\ l_{2} & = 1 \end{aligned}$

Blender Mathematica

Ideal Double Pendulum

Boundary conditions

Kevin Steiner

Physics student