Circular variable dependency in Vehicle Dynamics 3 DOF Dual Track Block.

In the dual track 3 DOF block, the documentation provides the following 4 equations:

First of all, the 3rd equation seems to have been copied from the single track documentation, and doesn't properly account for the left and right wheels. But I would assume that I can just replace xf and yf with xfl and yfl, respectively, and the equation will still hold.

My real problem is that the first equation uses , but then the equation for ultimately depends on the result of that first equation.

I'm not quite sure how to resolve this circular variable dependency. Does just use the previous , and then the resulting force is used to calculate the current ? Or is it the other way around? Or are the equations just wrong?

Yet another issue that I'd be able to figure out if the vehicle dynamics blockset were actually open, and not implemented in P-code.

[Paul]

Where is Fzfl in the equation for yddot?

[Daniel]

It carries through equations 2-4, which is why I listed all of them.

Fzfl is in equation 2, the result of which is (or should be if the documentation was consistent) used in equation 3, and the result of that is used in the equation for yddot.

[Paul]

Ok, I'm following now. It looks like the doc page section for Dual Track -> Tire Forces needs some work. It either needs to show all eight force components explicilty, or it needs to explain that the four equations generically apply for both the left and the right.

Assuming the equations are correct, the implementation could be as you hypothesize with artificial delays introduced into the model in the p-code.

Another alternative is that the model could be set up to solve simultaneous equations for all of the unknowns at the acceleration level at each step, which would include xddot, yddot, Fzfl, Fzfr, Fzrl, Fzrr (at least as far as I can tell). I think (could be wrong) that these would be six linear equations in six unknowns. One could go through the work to formally setup A*p = b, where p is the vector of six unknowns and then solve p = A\b. Or the equations could be solved with other numerical means if one doesn't want to work through all of the equations to form closed-form expressions for the A and b matrices explicitly.

Perhaps the reference at the bottom of the doc page would provide some insight?