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The pages above discussed how to construct the matrix A that relates the elongations of each springs, e_i, and the movements of the masses, m_j.
I understood the material that's presented on these pages, and I do get the physical intuition behind the equations. For example e_2= u_2 - u_1 because suppose m_1 didn't move in a moment of time and m_2 moves downwards, then u_2 is ( ) and u_1 is 0 and the second spring will be stretched which corresponds to a ( ) elongation. But I have a problem in this subsection when the text starts discussing about circles of springs.
Based on the given matrix A, why is the first equation of the system e=Au is e_1=u_1 - u_3 and not e_1=u_3 - u_1?
Why is that when u_3 moves downwards and let's say u_1 is fixed for a moment of time, the spring that connects mass 1 and 3 becomes compressed (elongation e_1<0)? Shouldn't it be stretched? Can you help me understand the physical intuition behind this equation e_1=u_1 - u_3 ?
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