Sorry but that is a very sweeping statement to make. Hip problems are not purely confined to GSD's, are not proven to be genetic and in most cases do not result in the dogs falling over. There is a condition called CDRM (or more commonly these days DM) which can cause rear end problems, again in many breeds. You can only tell if a dog has hip displaysia is you have them x-rayed. A dog with hip displaysia would be in pain and would not be falling over and then getting up again as though nothing has happened. Smaller breed like Jack Russells can suffer from patella luxation, where the knee joint is not stable (often called the Jack Russell 'Hop') but again is evident in many breeds. A stroke would not affect just the hind legs, it would more likely affect the balance and the head and neck area, with lack of co-ordination much like in a human. Dogs with arthritis do not necessarily show pain, in fact many dogs don't show pain in any circumstances. Try getting her a Bioflow collar, which can help ease the joints and give her a supplement such as Denes Greenleaf tablets, or Glucosamine and Chondtroitin, and either of these will ease the symptoms of joint pain and stiffness.