The problem is, I don't know how to apply the solution they provide.
It's because your variables are static i.e. they belong to the class, rather than to an instance. Take a look at Java Tutorials | Understanding Instance and Class Members for more information about what this means.
You should remove the static keyword, so that they become instance variables.
Sure, the original code contains a medium-size class file, collision detection and physics. I'll try to simplify it down to the heart of the problem and post it here.
Although symptoms were the same as the ones reported in the link I've posted, the cause was entirely different.
It turns out my whole class code structure was wrong.