Hips can affect the lower back in two ways: one is when there is an imbalance between the left and right hips, as mentioned in Lower back pain and Alignment and the other is when both hips are weak and tight, and the pelvis is not stabilised correctly, or pelvic movement over the head of the femur (the Coxo-Femoral joint) is limited, causing the lower back to be over-used in extension movements. Yogis, and athletes in general will wonder how this is possible, especially if they do exercise to strengthen the hips, but their problem never improves.
Weakness and tightness in the hips can be created by injury, but also occurs in any athletic activity, if there is a focus on the legs, with not enough core body strength to balance. If the postural muscles in the legs, namely the Hamstrings and Hip Flexor muscles become strong and tight, they inhibit the stabilising muscles in the hips by Reciprocal Inhibition. Please refer to Reciprocal Inhibition and the Hips for an explanation. Tight Adductor muscles inhibit the Gluteus Medius, which can lead to knee instability as well as pain in the hip and an inability to stabilise the pelvis in a horizontal plane.
It is not simply a matter of stretching the stronger leg muscles, people with weak hips cannot stretch their leg muscles adequately, and is one reason why some people can’t get into Hanumanasana, Kurmasana, or Samankonasana, or some are able to do Hanumanasana, but find Kurmasana painful or impossible. If they force these postures, lower back pain is inevitable. Hip strength must be adequate for leg muscles to lengthen without injuring the lower back.
Professional assessment and treatment is usually necessary, because hip weakness can be limited to a specific side, or set of muscles and the body learns to compensate, for example: it is quite possible for the hamstrings and spinal extensors to extend the hip and leg without using the Gluteus Maximus and these motor patterns become fixed and persist, meaning that correct muscle use has to be relearned. Sports professionals like Biokineticists are best equipped to deal with these problems.
Standing balancing Asanas like Utthita Hasta Padangustasana and Vrksasana maintain a balance of hips and legs, but care must be taken not to overdo lunging postures of all kinds, these tend to strengthen the legs, at the expense of the hips, especially if they are held for long periods of time.
Reading sources:
De Franca, 1996, Pelvic Locomotor Dysfunction
Cook, 2003, Athletic Body in Balance
Sports Injury Bulletin
Yoga Anatomy for the Perplexed 