@Denny Phillips - walk more. Build up gradually and don't do it to the point of fatigue, but walk. It'll help.
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Just in general, driving your heels and standing up straight with swings does a lot for me. I generate a ton of power and it keeps my shoulders down. I noticed I was shrugging when I first started, so no bueno. I always think "stand tall" as my hips go forward. The body just does what it needs, including keeping my abdomen tight.@StuKE, you have seen a doctor who has given you permission to do kettlebell swings, yet kettlebell swings cause you pain.
Step 1) Stop swinging until you have seen your doctor again and are sure you haven't caused any damage, then work with a competent instructor, and I strongly recommend one of ours.
One possibility is that, because of your repaired injury, you will have a smaller margin of error in your swing performance than others. You ask if anyone else has experience with this - yes, I had both a severe herniated disc and a double inguinal hernia but it hasn't stopped me from performing kettlebell swings or barbell deadlifts.
Those "odd pains" stopped once I started doing strength training the StrongFirst way - I used to have them.
Step 2) Strong abs are indispensable in keeping a less-than-perfect middle of your body working. You might consider doing some direct ab work, perhaps even making it your focus for a few weeks before trying the swing again.
Step 3) Consider working on the barbell deadlift instead of the kettlebell swing. It is easier to manage your body when moving it's slowly than when it's moving quickly.
You will notice in S&S that the kettlebell deadlift is taught before the swing. When I am training someone with a bad back, I prefer to go further with the deadlift before starting the swinging, usually introducing the barbell and making sure my student can pick up something quite a bit heavier than a kettlebell in good form. Your description of your hernia issues makes me think that same course of action might work for you, but again, quality instruction and tremendous attention to detail are required.
Step 4) Don't "thrust your hips forward." Drive your heels hard into the ground, keep pushing them into the ground, and stand up straight.
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