Question: The output resistance of small signal model for common drain JFET amplifier equals $$ \frac{1}{g\_\text{m}} || R\_{\text{ds(on)}} \parallel R\_\text{S} $$ and since $$ R\_{\text{ds(on)}} =\frac{1}{g\_\text{m}} $$ we can also write this formula as \$\frac{1}{g\_m} \parallel \frac{1}{g\_m} \parallel R\_\text{S}\$ right?

Which could be derived to $$R\_{\text{OUT}} = \frac{1}{g\_\text{m}}/2 \parallel R\_\text{S}$$ right?

![enter image description here](https://i.stack.imgur.com/vZLUW.png)

Answer: 
As an EE that works with lithium-ion, we don't charge our batteries at temperatures that low, typically the software is set to disable charging below -20C to 0C, depending on the application. We make some batteries with resistive heaters in them, which allow operation at temperatures as low as -40C to -60C after a short warming period. I do know that the cells can be charged at a very low rate when they are cold, however it's generally viewed as a bad idea and causes unnecessary stress on the cells.

Bottom line:
Is it possible? Yes, you CAN charge them at a very low rate(~0.02C) at -30C.
Should it be done? No, I don't recommend charging them cold as it causes unnecessary stress. If you intended to go the route of heating them, you need some "smart" circuitry that only charges them when they are warm enough(I would recommend around ~0C).
Yes, you will damage the battery if you charge at low temperatures (beyond the product specification). You can read this if you only believe research papers: <https://www.researchgate.net/publication/282407632_Optimal_Low_Temperature_Charging_of_Lithium-ion_Batteries>

If you are using solar to charge the battery, then of course you could use solar power to heat the battery. It makes your charging design a little more complex but it would not appear ridiculously so.