When I don't do this, I feel it in my body-- unfortunately at about 1am.
I wake up with energy laying in my back, wanting to move my legs, my body. My mind wanders during this time and I have a hard time turning thoughts off. Needless to say, this is not enjoyable in the middle of the night. Since I have started working full time a few years ago, I find myself skipping this practice occasional. Again, not a good idea, because often when it is skipped is when I need it the absolute most...busy days, overflowed with scheduling, that leaves me mentally drained.
When I do these simple asana's, then my sleep is vastly improved. I stay in each pose for about 2-5 minutes. I generally let my mind wander, letting go of the day and observing what is showing up on my nighttime mat. Things that I need to let go of before bed, so they don't want to chat in the middle of the night.
Enjoy. Om.
Uttasana
Tarasana
Savangasana (with variations)
Savasana