The only pushing element I can think there was, is when one side would try to exploit the death of some opponents in certain areas, and so "pushed" men there to distrupt the enemy's phalanx formation...
BTW about grips, underhand can't be the case with an aspis, especially undershield, due to its size, while overshield will expose so much the arm and shoulder with an angle that makes any shoulder guard useless...
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