It is possible, but it will require a bit of work to implement it. Sorry I can't share a scene file on this at the moment.
You would need to use a sopsolver (but only for the points that you will be instancing/copying/delayed loading your pieces onto)-> you need to iterate over time, so you can't really get around that.
Alright, you don't really need a sopsolver, you could use simply update the point along the arc defined by the equation by using $FF or any parameter/slider you want to link to it. I find sopsolvers handy as they allow me to store a history and calculate/trigger all kinds of other secondary usefull information + once it is cached you can scrub.
In terms of visualisation you could previs by building the lines/arcs first and then use a carve sop to extract points from those arcs. This is of course heavier and less accurate than using the equation to get the point - but you see what you are doing.
This will help you get more speed: declare all your attributes on your initial geometry, do not create any new attributes as you go as this slows the multithreading of vex. When points become inactive, delete them from the simulation so they are not going to be calculated - this progressively speeds up your sim.
In regards to your attributes, make sure you update your up vector and N over time otherwise you will have issues when you need to instance your objects onto it. You can sort of give it a fake orientation linked to the change of rate of v, but that doesn't always work.
You can previs the paths of the pieces as they are just lines mapped to the equations of the trajectories. In terms of coordinate system all the wiki stuff is "2D", I would recommend sticking with that and add the 3rd coordinate by converting from x,y,z to polar coordinates. That way you are left with: angle of elevation (this will define your arc) and angle of rotation (generally around the y-axis, this will orient the initial v to face the target).
This will help you map those curves:
In terms of control it is up to you if you rather set the initial velocity and/or angle of elevation, or if you rather use a target point that the piece is supposed to hit and calculate the other attributes from that target point.
This hopefully gives you a starting point.
Edited by pclaes, 23 December 2010 - 05:23 AM.