Sorry for this very simple question but I am still very new to the laws of motio

Question

Sorry for this very simple question but I am still very new to the laws of motion.

I am dealing with 2-dimensional vectors in my programming environment and I'm following these slides to learn about simple integrators.

Near the end of the slides for the 4th Order Runge Kutta Integrator he is calculating acceleration like this:

a2 = acceleration(p2, v2)

However, I'm not quite sure where that function is defined in the slides. I'm sure the answer is very simple but for all prior slides the acceleration was always constant.

Explanation / Answer

That function is not defined there because you want to use a different one, depending on what kind of motion you're modelling. Using the obvious Newton law
a?F,
you can think of it as calculating the force that acts on your object, e.g. the spring force. In the case of gravitation, you simply put in the constant gravity acceleration downwards.

(I'd like to note that in this case, 4th order Runge-Kutta is something of an overkill as 2nd order is already exact! But it's nevertheless a good idea to use it here, to be consistent: 4th-order Runge-Kutta is used in a very wide range of applications.)

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