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This program was created by Adrian, one of my top students in both physics and programming, as part of his programming project.
At Katedralskolan in Uppsala, where I teach, we have a full-year course in programming. During the course, the student learn about how computers and programming work. We begin with a brief introduction to programming in Assembly language (see ELIAC I), but the primary focus of the course is on JavaScript and HTML. During the spring term, the students do their own programming projects, and this is one of the best projects I have seen so far.
This project, along with his achievement in physics, earned him a Sigbaum diploma, which we hand out each year to our top physics student. This diploma is in honour of the Nobel laureate Kaj Sigbaum, who was a former student at Katedralsolan.
I had a little problem deciding where to place it, but I ended up placing it in the chaos and fractals section.
Here is a description of the program by Adrian himself:
This program simulates the motion of a double pendulum using numerical methods. By allowing multiple pendulums to be simulated simultaneously with slight differences in their initial conditions, the program serves as a powerful tool for visualising chaos and the famous butterfly effect.
In order to simulate a double pendulum, one must solve its equations of motion, which form a system of ordinary differential equations. These equations unfortunately have no analytical solution and must therefore be solved numerically. This program uses the 4th order Runge-Kutta method (RK4), due to its accuracy and efficiency in solving such equations.
In addition to the double pendulum, the program also supports simulations of a simple pendulum, as well as both simple and double pendulums connected by springs. However, please note that energy measurements for the spring pendulums are not accurate.
The program can display graphs of kinetic and potential energy over time, as well as a plot of θ₁ against θ₂, which tends to display distinct and interesting patterns for small initial values.
Upon opening the program, you’ll see an info button marked with a question mark. Clicking this button will display the controls and highlight some of the program’s main features.
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