If you do not have a strong low back to act as an fixum putnam or fixed position one would not be able to generate enough force to complete most tasks in space.
Proper movement of the pelvis in particular is critical in the gait cycle. A misalignment of the pelvis due to muscle imbalances between the abdominals and the low back can cause a huge reduction in a runners performance independent of cardio fitness level.
A low back exercise to ensure that your low back muscles (or posterior abdominals) will limit pelvic tilt and creating proper pelvis rotation is a Back Extension Press-up. I want to make sure that you do not confuse this with a normal push-up. In yoga it is referred to as a Cobra Push-up. This is a great exercise for anyone who has pain shooting down the leg. This will reduce that and get the pain to move toward the back (this called centralization) and eventually result in no pain.
The primary muscles that will be involved in this exercise is the errector spianae group and gluteus maximus.
The secondary muscles that will plat a part in this exercise is hamstrings, rectus abdominis, external obliques, and internal obliques
To perform this exercise follow the following steps:
1. Lie face down on the ground with arms in the push-up position and legs outstretched. (maintain a rigid body in a straight line)
2. Press up with the arms only until the torso is off the ground. Hold this position for 10-15 seconds, maintaining normal breathing throughout
3. Lower arms, bending at the elbows, and return to the original position.