Dynamic Modeling of AWD CAR

I am fascinated by Bond-Graphs and how capable they are, They are a graph representation of dynamics/kinematics and they work for electrical, mechanical and even chemical systems.

if you are familiar with mass-spring-damper system dynamics, this is how a bond graph for that system looks like,

very simple right? one connection node in the middle and four other elements.

I used similar techniques to extract a detailed model for an all wheel drive car, the graph looks like

and lateral and longitudinal friction models can be drawn as (based on stribeck friction model)

and eventually you can use a software package to convert the graph to analytical equations (I used 20Sim). one could simpy write a solver themselves.

Runnig some simulations of this ODE gives reasonable trajectories for the vehicle. Here is a simulation of one equilibrium point on the equilibrium manifold

You can find a c++ implementation of mentione ODE here