I don't think there is any reason to make different things for visualizations at t=t1 versus t=t0 versus t=[1, 2, 3, 4, 5]. You're methods should accept any numerical values of t and output equations (functions of q) to generate the visualization. If you supply values at one instant of time then you get a static visualization, but if you supply lists/arrays then you should be able to play the animation through time. These are not distinct cases (static viz at one config and animations). A static viz is just one frame of the animation.