Walking & Swinging How can I show that the most convenient way to move the arms while walking is swinging them back and forth, alternatively?
To pose the question in another way: can I prove, starting from the conservation of momentum and angular momentum, that given a rigid solid body moving at constant speed and with two appendices on the side, this appendices will move as our arms do when we walk "freely"?

 A: This is a responce to usumdelphini's comment:

Is there a way to show this formally, without relying on experimental data?

I'm not going to attempt a deep analysis of walking, but it's fairly straightforward to show that using your arm reduces twisting. Suppose you're looking down on the person walking from above, and suppose they're a cylinder $^1$. Then you'd see something like:

When you move your right leg forward this takes some force $F$, and by Newton's third law there is an equal and opposite force on the point where the leg is attached to your body (the green dot). This causes a torque on your body of:
$$ T = Fr $$
and as a result your body will tend to twist clockwise.
Now suppose you move your left arm forward at the same time:

Moving your arm creates a torque of $T_{arm} = fr$ in the same way, but the torque is in the opposite direction. So the net torque on your body is:
$$ T = Fr  - fr = (F - f)r $$
and the result is that your body will twist less.
$^1$ traditionally we assume everything is spherical, but I'll make an exception in this case
