I've been learning the priority of keeping my spine long over everything else posture-wise in the sun salutation sequence. Consequentially, for flat back, I keep my hands on the floor at the level of my little toes but my knees are bent enough so that my back is not rounded but straight, tilting my tail bones up and my collar forward. I keep my arms very straight with some pressure on the hands. I prefer to have my hands on the floor by my little toes so that they are in position for high plank. When doing downward dog, I keep my dog long meaning my hands are very far from my feet. I accentuate tilting my tail bone to the sky. My index fingers are facing directly north, straight ahead. I try not to let my upper arms collapse in, I bend my knees a lot when doing this. My hamstrings are tight and once again, bending my knees allows me to keep my spine long. Flat back and downward dog are the two positions of the sun salutation sequence that I've made some modifications with for myself. Hope this helps you.
Depending on the type of lower back pain you have, you might need to modify it differently than I do. I have a herniated disk in my lower back that is chronic but usually OK. Depending on the day, the only two poses that I sometimes have trouble with are the standing forward bend and upward facing dog.
For standing forward bend, I make sure that I only fold as far as I can for the day while keeping my lower back flat (not rounded) This often means that for the following pose (flat back) I put my hands on my shins to give me the leverage. Usually over the course of a yoga practice, my back loosens up enough that I can get my hands to the floor, but I start out slowly.
Then, in upward facing dog - this one usually feels good on my back, but occasionally not, in which case, I substitute Cobra until my back loosens up.
An extra tip: For downward facing dog, my yoga teacher suggested that in setting up this pose, I bend my knees a little bit and arch my back a little and thenn straighten the legs keeping the slight arch. He calls it "putting some upward dog in your down dog" - It is subtle, but helps to protect that you don't round your back in downward dog.
I also don't jump in or out of downward facing dog, as I don't have the core strength yet to do it properly and controlled, and to really "jump" at this point is jarring on my back.
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