Define position and orientation in a local coordinate system Suppose we have a world coordinate system W and a 3D model m1 defined in W. m1 has its own local coordinate system L.


How would we define L? Only by the transform from W to the object?


If we add a 3D model m2 to W : How do we define its position and orientation in L without worrying about the world coordinate system. Like just saying for instance that it's in (0,0,0) in L? 

PS : If it's possible using algebraic or 3D geometry matrices transformation equations ?
Assuming that your 'models' can be represented by collections of points, then these points' coordinates are defined with respect to some coordinate system. You said that $m_1$ is defined wrt the coordinate system $W$. And you have some other coordinate system $L$ and want to find the positions of the points of $m_1$ in it. To do this you need to multiply each of your points with the matrix used to go from $W$ to $L$. To build this matrix you need to know the coordinates of the basis vectors of $W$ wrt $L$. Then you can make a 3x3 matrix where each column is a basis vector with which you can go from $W$ to $L$. Note that a translation will also be necessary if the origins do not agree.
The solution for $m_2$ is similar.