Another thing I'd add is that the bicycle model can take take may forms depending on what you want to model, what information you have available and what you want to investigate.
At the base level is the classical linear, constant cornering stiffness model in Milliken (chapter 5) and Guiggiani. It's the fundamental tool to understand the 6 lateral and yaw derivative gains which are in turn the fundamentals of lateral vehicle handling dynamics. It's the simplest and therefore least precise model but if you don't understand it then you won't understand anything following. The job of a vehicle dynamics engineer is essentially the management of the front and rear cornering stiffness' in every situation and the linear bicycle model represents this in it's purest form.
The linear model can be solved statically without iterations, so you can use simple tools like excel to model it. Any input condition (velocity + steering angle) will only result in one response.
Many people would suggest that the linear bicycle model is useless for motorsport but this is not completely true. You just need to work with it differently. For example if you interrogate your tyre model (I assume you are part of the TTC?) to find the cornering stiffness at say 85% of max lat then you are able to construct a model representative of the vehicle operating at 85% of it's lateral capability (there's a bit more to it than that but the concept is correct).
The next step in complexity is a non linear tyre model. This doesn't necessarily mean a fully parameterised Pacejka model, there are simpler versions of Pacejka (4 parameters) then there is TM-Easy (polynomial based). These are more complicated and generally must be solved in the time domain using a dynamic solver (still feasible in excel though) because the problem is no longer statically determinate - there can be more than one solution to the response of the vehicle to a given input condition (velocity + steer angle).
The non linear models are interesting because they define the peak lateral acceleration capability (which you don't see in the linear model) but more importantly the stability condition of the vehicle in that condition can be calculated by using the instantaneous cornering stiffness of the model in any condition of cornering. At this point your are able to objectify the trade off between grip and stability at the limit.
From there, both the linear and non-linear models can have the front and rear 'tyre curve' modified to include kinematic, compliant and load transfer effects which work to introduce more or less slip on an axle for a certain lateral load which in-turn changes the cornering stiffness. This is also outlined in Milliken. For example roll steer has the effect of increasing (for compression toe-in) or decreasing (for compression toe-out) the cornering stiffness at any point.
One final thing I'd add, which seems to often be overlooked in Milliken, is that the cornering stiffness of an axle depends on the axle's vertical load (it's roughly proportional). So as you move mass or aero loading front and rear, you are changing the cornering stiffness of the axles. This is the reason why cornering stiffness numbers which are not related to a vertical load are useless. You need to find the cornering stiffness' of the FSAE tyres at the vertical load that roughly corresponds to your static weight force.
Not the engineer at Force India