What do you do with your abdominal and leg muscles?

My natural tendency tends to be to stand, walk or run* with my back in a slightly lordotic posture and my stomach muscles relaxed.  I can tell I tend to sway a bit when standing, and I suspect I'm worse than average in that regard.  If I rotate my pelvis very slightly forward/upward this puts some light tension in my abs, without feeling like I'm straining to "crunch" them, and if I think about standing a bit tall, that seems to tighten up my leg muscles just a bit.  Together, I feel like this firms up my stance without it being "tense."

Does this seem like I'm on the right track?  What is the conventional wisdom for establishing a stable stance?

I'm not a great athlete or body-builder, but I go on 4 to 5 mile walks or do middling weight training sessions with body weight and dumbbells (usually dips, bent-over rows, sumo deadlifts and/or split-legged deadlifts, push-ups, sometimes Romanian deadlifts, lateral raises and overhead press) at least three or four times a week, so I'm probably in better shape than the average 58-year-old.

*Twenty-odd years ago, I was surprised that I could go for a 30' trail run without problems, but if I tried to run on a flat surface, my knees started to burn within a hundred yards.  I went to the sports medicine clinic, they had me run on a treadmill, and, when they could stop laughing, said that because my waist was too relaxed, my hips were wobbling around like crazy and making my knees twist from side to side.  Doing the slightest activation of my abs solved the problem.  When trail running, my whole upper body was slightly tense because I was prepared not to trip over the next rock, root, or small deviation in the surface, so that was why I had no knee problems then.

I generally leave them in place. Taking them out before the match is terribly messy

When I was taught how to shoot bullseye in the late 80's, the stance was very relaxed. Lean back to counter the weight of the pistol and if belly was pooching it didn't matter. Very relaxed stance.
Modern stance is tight core and all body muscles firmed up for support. Standing more erect.
Both are learned stances, not natural in my opinion.

Seek out a local Master bullseye shooter to give you some guidance. I catch many shooters twisting slightly at the hips that otherwise they would've never known.

Jon

Jon Eulette,... I catch many shooters twisting slightly at the hips that otherwise they would've never known.

This will cause tendinitis or bursitis. Bursitis is quite painful, takes a long to to get over and usually involves seeing a physical therapist. I was twisting my hip as an unconscious attempt to 'lock' my lower body trying to be rigid.

I'm no master, but I find a relaxed stance beneficial.

Squeeze your glutes

Yes, I think you are on the right track. I had to look up lordotic posture. I call it "sway back" and I have the same tendency. Rotating my pelvis forward eliminated my back pain after standing and shooting all day. I can't say that it improved my hold, but I am sure it didn't hurt.

I wrap my left arm across my body and grab my belt and my right pants pocket with a little tension on the arm and a little tension in my abs / core. That also helps counteract my sway back and definitely makes me more steady. Unlocking my knees slightly also helps.

I was thinking about buying a girdle after seeing my posture in one of Steve's pictures from Atterbury. I will start with his method above, first.