This animation was produced in response to a video of real pendulums performing similar tricks:
Not having an animation program I thought I’d use the finite element program Strand7. Modelling the pendulums was easy, just 15 beam elements with a “translational mass” attribute on the end (more on the exact length of each pendulum later).
Strand7 will perform a dynamic analysis, so I could have given each pendulum a displacement and then carried out the analysis of their movements over 90 seconds, but because I was only interested in generating the patterns in this case I decided to take the easy way out and generate the pendulum movement by inputting the displacements directly. The procedure was:
- Set up 30 “freedom cases”, each with the lower end of a different pendulum given a unit deflection in the X or Y direction
- Set up a series of 1800 increments, corresponding to time steps of 1/20 second, and factor each freedom case to replicate the pendulum motions.
- Run the analysis
- Create an animation of the resulting pendulum motions, using an end on view as in the original video
The only remaining problem was how to enter 1800 x 30 factors quickly and accurately. The solution (naturally) was to set up a table of the X and Y displacements of each pendulum in Excel:
These factors were then transferred into Strand7 using the program’s API (the use of which I will describe in more detail in later posts).
The only remaining detail was to find the correct pendulum lengths to generate the patterns I was after. After a little experimentation it became clear that each pendulum much have a different integer number of cycles over some fixed period. I fixed the first pendulum length at 350 mm, which has a period of 1.187 seconds, or 51 cycles over 60.558 seconds. The other pendulum lengths were then adjusted to have 52 to 65 cycles over the same time period, giving a range from 336.7 mm to 215.5 mm.