## Adapt the MBS conventations and notations

Fro the moment, the notions of independent, dependent and driven variables is clear but could be clearer. The driven variable although they represent additional constraints are treated as a special type of independent variables. This leads to the partitioning of the independent variables and the second reduction of the equations of motion.

If this is clear in most Robotran developer heads, it is not obvious for the users especially for the students. The fact that the independent variables which are not driven does *not* have a specific name, complexifies the learning of the users. In addition, it also leads to misunderstanding among the developers as no symbol is associated to this famous "independent/non driven" variables. The lack of proper convention from our part leads to an additional complexity for the users and I think it should be fixed.

Proposed solutions:

- u, independent

-- f, free

-- c, driven - v, dependent

OR

- u, non-dependent (in the sense that they do no dependent on other variables through a kinmatic constraint)

-- f, independent

-- c, driven - v, dependent

I personnaly find the second solution more elegant as the notion of non-dependent and independent should draw the attention on the fact that there is a subtlety to understand.

In addition, the notation for the "first order" state vector should be clarify. For the moment, y,x and z are used in the time integration, the equilibrium and the modal analysis. Sometimes the order is [vel,pos] and sometimes [pos,vel]. This should be uniformized also in the stateSpace submodule.

The notation regarding the invdyna process and the Qq, Qa and Qc should also be revised.

In addition, we could think about a way to clarify what is inside the mbs_data structure. I think that it could be nice to separate the model variables (mass, lengths, ...) from the state variables (jointForces, joint coordinates, vel and acceleration). If not done in the code, it should at least be specified in our Documentation.

- Fix the indpt,dpt,driven problem. Change it in all supported codes, course and documents.
- Fix the ordering in "first order" state vector y,x,z and clarify their definitions.
- Fix the invdyna symbolic naming and Qq,Qa,Qc
- mbs_data splitting to better understanding of what there is in it.