The benefits of Downward Dog are well known. Reversing the pull of gravity on the body, and weight bearing in to the arms can do wonders for an unhappy spine.
By using the hammock to traction out the pelvis in this position, the body is supported in it's search for alignment and length. Using the feedback of the hammock on the hips to keep them aligned can make all the difference as we engage the legs, reaching them away from the body in order to traction the back. When alignment is found, the entire body feels it ; effectively teaching the leg muscles how to support and decompress the back.
Inversions are known to sometimes cause a mild euphoria, as well as dizziness at first. Take it easy, and use the hammock as support when coming out of this position.