number of independent energy-storage elements in this circuit?

So I practiced various examples of modeling electrical cricuits and mehanical circuits. I stumbled upon this one:

and it's same as this:

now with these direct substitutions: $$k=\frac{1}{L},\;B=\frac{1}{R},\;J=C,\;T_{(t)}=i_{g(t)}$$ I get these equations: $$i_g=i_{l1}+i_{l2}$$ $$i_{R2}=i_{l2}$$ $$i_c=(i_{R2}+i_{l1})-i_{R1}$$

I get this circuit:

Now, which number of independent energy-storage elements is in this circuit? Which order is differential equation which describes this circuit and how it looks like? I got this: $$i_{g(t)}=i c+i_{R1}=C \cdot \frac{d uc}{d t}+i_{R1}=C \cdot \frac{d u_c}{d t}+\frac{uc}{R{1}}$$ Is this differential equation which describes this circuit?

• It's clear right off the bat that the equation is missing something, because the inductor elements are not considered at all. Consider this technique for efficient analysis in lieu of writing differential equations; it scales very well to the three storage elements in your design. Commented Dec 10, 2020 at 5:17
• Since a current source is driving the two parallel branches, the current of the two inductors are related by the algebraic equation, $i_{L1}+i_{L2}=ig$. So I would say that the two inductors together contribute only one effective energy storing element. Also, how sure are you about the correctness of the mechanical to electrical conversion?
– AJN
Commented Dec 10, 2020 at 7:11
• @AJN to be honest with you I'm not sure for it but anyway, regardless of mehanical to electrical conversion, I wonder how this electrical circuit can be solved and ofcourse if someone sees that this conversion is incorrect it would be nice to notify abot mistake. Commented Dec 10, 2020 at 8:27
• WTH does this mean? You're applying a torque to an inductor? Commented Dec 10, 2020 at 20:21