RK4 for getting the position of a particle, and then animating it

Hi everyone,

I'm relatively new to C++ but I know the basics. I want to use C++ to integrate equations of motion using a Runge-Kutta method because I know it will be fast. Afterwards, I would like to animate the trajectory of, say, a particle in 3D space. I want to have a real-time simulation if possible.

It would be much appreciated if someone could guide me to the simplest way of executing these two tasks. I think I am capable of writing the code for the Runge-Kutta integration, but I don't know how to animate the position vector in time.

Looking forwards, I will eventually have several points along a line, that I will connect with NURBS most likely, and I will be wanting to animate that. Even further, I will be wanting to animate the surface of an object such as a cable, most likely using a NURBS surface, unless there is a better option. I am adding this paragraph so that you can hopefully get an idea of the complexity that I'll require later on, so that I can animate my simple particle using the same environment.

Thank you.
I would think that Vulkan or opengl is what you want:

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