I think what he is looking for is the output to go to zero, not just go unregulated or drop to 1.25. Disconnect the input if it drops below 10 V?To do this you will have to add a comparator to the input. Why don't you sketch up a block diagram or schematic for us to review.
Also, what do you mean by "cut out"? An LM317 has a minimum output voltage of 1.25 V. You can not turn the output down to zero volts without more modifications to the standard regulator circuit.
Automatic restart is not a problem. Do you want the system to restart as soon as the solar panel output is high enough to run the system, or wait until the battery is recharged enough?i will like arduino to stay off until sunshine and battery is recharged enough to power the arduino
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