[color=#008486]This GeoGebra book is the English translation of the Spanish GeoGebra book "El dominio del tiempo" ([url]https://www.geogebra.org/m/nfjy7ug4[/url]), which contains the material from the lecture "Perpetuum mobile" delivered at the 5th National GeoGebra Day held in Cuenca, Spain, on October 4th and 5th, 2024.
This content is also available in its (Spanish) original format used during the lecture at: [url]https://geogebra.es/pm/[/url]
In this book, various [b]real-time[/b] kinematic experiments are simulated involving a mass at position [color=#1551b5]M[/color] with velocity [color=#c51414][b]v[/b][/color] subjected to an acceleration [color=#0a971e][b]g[/b][/color]. The animations [b]do not use formulas[/b] (neither equations, trigonometry, nor differential calculus); they only implement the necessary variations in the vectors that direct the motion. These variations essentially reduce to the execution of two instructions:
SetValue([color=#c51414][b]v[/b][/color], [color=#c51414][b]v[/b][/color] + [i]dt[/i] [color=#0a971e][b]g[/b][/color])
SetValue([color=#1551b5]M[/color], [color=#1551b5]M[/color] + [i]dt[/i] [color=#c51414][b]v[/b][/color])
where [i]dt[/i] is a very small time interval (a few hundredths of a second). In other words, every short time period, [color=#c51414][b]v[/b][/color] changes by an amount equal to "a little bit of [color==#0a971e][b]g[/b][/color]" and the position [color=#1551b5]M[/color] of the mass shifts by "a little bit of [color=#c51414][b]v[/b][/color]". It is important to note that these sums are not numerical but vectorial, meaning a certain quantity is added in a certain direction.
We will see that this idea, presented as variation tables by Richard Feynman in his famous book [i]The Feynman Lectures on Physics[/i] (Volume I, 9-7, [i]Planetary motions[/i]), can be perfectly adapted to animations made with GeoGebra, thanks to the ability to synchronize with the user's computer (or other device) clock. This allows for a fairly accurate simulation of various situations without resorting to higher mathematics.
Rafael Losada Liste
GeoGebra Institute of Cantabria[/color]
