That Seems awful complicated to me.
All I do is Place a car on the ground. What ever curves you need you put in your walk path. Then from the top camera pull away so you can see the whole scene. (the numbers are for Example only.) a thirty frame animation. Frame 1 the car looking from above. line the car up with the walk designer path. Then at frame (between 10 and 12 - and 18 and 20) depending on how tight of a curve you want to make it. For example sake, use frame 12 which is before the curve using the Y Rotate and and X & Z Trans. pull your car to that position and line it up in line with the walk path. and I use spline break then go to frame 18 and again line the car up with the path and spline break it again. finaly the end frame pull the car to that point and line it up again and your done.
I have as smooth of a turn as you could want and can do the hole thing in less than a minute.

If the subject should be a rocket going up, then down. the same applies as when you are looking down from above only I use a side view camera. I all ready have the turns completed, now all I have to do is bring the walk path in the air while Im in the side view camera.
From there I use a side view to raise the craft in the air lining it up with the walk path then use the Rotate X to line up with the arch with the peak of the path. using the same steps as above and bring it down.

When you get into math that becomes confusing. If it looks correct to the eye. that is what counts in animation. I wish I was good at the calulations use use. I could sure use them on other things!