Pickett's Charge Motivation?

In specific answer to your question, the same thing that motivated you when you served. By the time the $hit hits the fan things like patriotism and politics mean very little to the troops. They fight because their buddies on either side of them are depending on them for support. Lee's troops believed in their cause, it was what motivated them to enlist in the first place. But after the First Battle of Bull Run the immediate motivation was to the unit, and more specifically to the men you were fighting with directly in your company, platoon, and squad. That's true of all soldiers and all wars.

Contrary to popular opinion, I believe that Lee's tactics were sound.

Here's how it should have gone:

Lee makes a diversionary attack against the Union right flank and sends his cavalry force around the flank to attack from the rear. The Union forces move to counter the diversionary attack and Lee's artillery bombards them in transit. Having thus decimated the Union forces, Picket moves in from the south to envelope and destroy the enemy.

Here's how it went wrong:

The Confederate cavalry was stopped by Custer's (totally irrational) counterattack. The Union forces did not move into the position which the Confederate artillery expected and instead reinforced their southern forces ... which left Picket in the untenable position of trying to take a reinforced line.

To answer your question directly, it is my belief that Lee (and Picket) believed that the attack could have worked (given their belief that the cavalry was already attacking from the north and that the artillery barrage had been successful).

There might be a strong bond of camaraderie between you and your colleagues, but how would you feel if you had an officer who continually made mistakes, put his men into needless danger and quite clearly was not up to the job? That would defeat your motivation no matter how strong the bond was to the others in your unit.

The Army of North Virginia loved Robert Lee, he sided with their cause and opted to fight for his home state - Virginia when it seceded. He could have accepted Lincoln's invitation to command the Army of the Potomac but refused (and in so doing left hanging one of the great "what ifs" of American history). Moreover he led his army through several battles where they outfought and outsmarted much bigger and better armed Union armies and by the time of Gettysburg had seen off several Union commanders. But, you also have to look at Gettysburg in the context of what had gone on before it - in the Chancellorsville campaign he committed one of the great potential mistakes in warfare - he split his army in the face of a larger force and in so doing won a fantastic victory. Clearly the men and the officers in the AoNV trusted him totally. So when on day three he suggested, or rather ordered a full frontal assault on Cemetery Hill the men accepted it because they believed that he knew what he was doing.

They also accepted the necessity of invading the North, knowing that to sit and wait in the Confederate States where they had continuously defeated several Union armies would only invite another army and then another after that until worn out and depleted they had to surrender.

Then you have to look at the nature of Gettysburg as a battle - unlike many other CW battles there was nothing planned or deliberate about it. Lee's army got sucked into a fight almost by accident and it then escalated from there. Consequently a lot of his army was not lined up as he wanted it - JEB Stuart's cavalry had been sent on a reconnaissance mission just before the battle and were absent and out of contact for all of July 1 and July 2. This therefore was an improvised battle where Meade and Lee were fighting each other almost blind with units joining in as they arrived. Had Early attacked and taken Cemetery Hill on day one the battle could have ended early most likely with the Union army retreating, had Little Round Top fallen on day two then the battle would have been fought differently from then on. These things didn't happen, the Union army fought well defensively and held on and having tried outflanking moves on days one and two Lee opted to go through the middle on day three. He also wanted the Union artillery to be neutralised but that didn't happen as planned, his strategy then called for a march and then a trot and then a suicidal charge across a mile of open ground. So why did he order it? He wasn't stupid and knew the downside but his army had never let him down before and while he knew they would take a lot of casualties he thought that they would overwhelm the centre of the Union army and finally inflict the defeat that was nearly there on days one and two and had been there at Chancellorsville and several other battles. Bear in mind that he also had a low opinion of Union generalship - Hooker, McClellan etc were timid and Meade, his adversary at Gettysburg, was no military genius. So perhaps tactical inflexibility, arrogance and a gamble that didn't pay off were his motivations. Longstreet and others counselled him against the charge, but they like the men who charged trusted Lee.

Sorry no references - this is just my reading and understanding of the battle. Unfortunately Lee never wrote his memoirs of the CW so we have nothing definitive as to what his motivations or decision making process was - all we can do is to look at how he fought earlier and subsequent battles and glean from that his experience, characteristics and personality traits that allowed him to get so far in his career, achieve so much and yet make this colossal and costly blunder.