Given the potential for being able to ignite a small, undiluted, and compressed fuel/air mix quite early in the outward stroke (perhaps a couple of degrees past T.D.C) I see hybrid attachments as possibly being not worth the weight, clutter and expence
 However... to collect energy that would otherwise be consumed in braking the Lullen-cycle motor could be used as a compressor and store energy as compressed air and then be using that same compressed air to operate the motor for a while as a compressed air motor and not be consuming any fuel during that time. Given the fact that, unlike other common motors out there now, the Lullen-cycle has virtually no deadspace created by a built in combustion chamber the motor could be used as a very effective brake.

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