When the Pandavas were all introduced in the rangbhoomi, they all had a special way of entering:
Yudhi: He jumped from the top of a building, used his spear as a pogo stick and gained some more air to do a spin before landing.
This shows that Yudhi is courageous. His using the spear as a pogo stick shows that he himself remains steady while distributing the effects around him. And his few aerial spins shows that even in dizzy times, he remains fully balanced (his landing style).
Examples: He was pretty calm during the whole dice game and the VH. He did have a freaky moment, but in the end he regained dharmic composure quickly.
Bhim: He enters and slams his mace into the ground creating a shockwave.
His entrance wasn't all too stylish, but he displayed his power. The symbolism from the shockwave is that he will absorb everything that comes his way and send a fair amount right back out
Example: he absorbed the effects of the VH and unleashed it on Dury and Dushy and the 98 other brothers
Arjun: He created a canopy of arrows above his head to shield himself from the falling elephant head statue. He then fired an arrow that collected Kunti's tear and returned back to him so he can put the tear on his head.
Arjun's entrance is very symbolic. We would call this lightness of hand, but actually it's pure dumb luck. Creating a canopy of arrows in milliseconds from no base is impressive, but that's what Drona thought. In reality that's not what happened. What Arjun did was he pulled back his bowstring and that created this force field around him that shielded him from the falling stuff. We couldn't see it because well ... the rocks were floating on the force field. This also explain how Arjun was able to shoot such a large arrow from beneath the rocks. He used the force field to raise the rocks, quickly shoot an arrow, and then reset the force field.
The arrow shot is also symbolic. After collecting Kunti's tear (which by the way, she didn't notice or react when the arrow passed by so close to her throat), the arrow began to spin (or it was already spinning, doesn't make a difference). Centripetal acceleration would essentially keep the tear from falling off, but the rotation of the arrow was significantly less than what was needed (since it was also fighting wind resistance, gravity, etc.. not to mention it pretty much curved around the arena).
Well ... I have no idea what this is supposed to mean, BUT worry not, there is still an analysis:
Did you notice how it takes 3 arrows for Arjun to freeze Dury back then, but it only took 1 arrow during the war. It shows that Arjun increased his power after marrying Panchaali.
That must be the power Panchaali brings to the table. Yudhi learns how to box, Bhim learns how to become humane after killing 99 brothers, Nakul has a good fighting sequence, Sahadev can wield a sword and make daring moves, and Arjun increases his power.
Nakul: He entered on a flying bird - let's call it a falcon because they are cool. The falcon is carrying him by the talons and drops him without him having to say anything. He hands on his crouched feet with the sword's tip touching the ground.
There can be two meanings to this: 1) Nakul was friends with the bird and they spoke the language of love or 2) Nakul was being carried to the bird's nest as a meal, but the bird accidentally dropped him. Nakul took out his sword because he wanted to kill the bird, but the bird dropped him.
We know that Nakul speaks horse and mouse, so it's possible he speaks bird too. But the point isn't that. If Nakul was such a horse person, he would have rode in on a horse. He either chose to or was forced to use the birdie. Or maybe he was riding on a horse when a bird picked him up thinking he was a handsome worm or something... This is another mystery we can add to the list of StarMysteries.
Sahadev: He had a running entrance with a toss / catch of the axe.
Enough said, he doesn't have much of a chance. Everyone else had a beastly intro and all he did was do a half a$$ed one item / one handed juggle. Pssh ... clowns can do better than that. His future was sealed already but he didn't know about it ... sigh ... it's ok Sahadev, some of us still love you, I hope.