Tesla coil is represented by these two 2║ order equations if resistance is R1=R2=0
(1/C1) q1 + L1 q1'' + M q2'' = 0 ("primary" net kirchoff equation)
(1/C2) q2 + L2 q2'' + M q1'' = 0 ("secondary" net kirchoff equation)
I know from two scientific articles that characteristic equation is:
(1 - M^2/(L1 L2) ) D^4 + (w1^2 + w2^2) D^2 + (w1^2 w2^2) = 0
with wi = 1/sqrt(Li Ci)
I couldn┤t find any source where it is derived and would like to check it. The problem is that I have no clue about how to get to that 4th order characteristic equation!
maybe a change of variable?
If someone could help many thanks.