TireSwing - Angle, Translation

[tropic granite]

Hi, does anyone know an equation to get Angle and Translation on a vector based on the logic of a swing. For what I'm doing I would need to get the Angle and Translation 20 times a second.

• https://www.teachengineering.org/lessons/view/cub_pend_lesson01

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[tardy portal]

Well, I assume you want to find θ as a function of t.
If θ is small, you can use the small-angle approximation and arrive at a linear second-order DE that can be easily solved.
If θ is not small, then the DE is only solvable with the help of non-elementary functions. More specifically, you need Jacobi elliptic functions. Here is a relevant article.

[tropic granite]

Thanks! 😄 I wasn't thinking that advanced right away, I just wanted a formula that uses gravity and air resistance to calculate Angle and Translation every 50ms

[tropic granite]

A little more specific, what I'm trying to get is a Vector3f (Translation) and a Quaternionf (Angle) from org.joml

• https://joml-ci.github.io/JOML/apidocs/org/joml/Vector3f.html
• https://joml-ci.github.io/JOML/apidocs/org/joml/Quaternionf.html

[tropic granite]

Thanks! 🙂 It looks quite advanced, so what I need can be quite simple ich really just need to take air mods into account, so when a user jumps on we increase the power up to a certain point and when it jumps off it doesn't get any more power and should slow down naturally. What I need is just an angle every 50ms really 🙂