What were the motivations of the Council of Trent? Are there any documents maintained by the Roman Catholic Church that provide the original (ie, by the councils themselves) commentary on the declarations of the Council of Trent?   

If not, what more recent writings, sanctioned or verified by the Roman Catholic Church, comment on the declarations of the Council of Trent?
For the same reasons as the councils before it, the Council of Trent was held to address current heresies and prevent schisms. Councils are held for the unity and benefit of the Church. Specifically, the Council of Trent was organized and held to address the budding Protestant Reformation and was part of a series of events and actions by the Catholic Church that some historians have dubbed the Counter-Reformation.

Pope Paul III addresses exactly what he hoped to accomplish with the council in his Bull of Indiction.

Among other things, the most notable item is in the first few paragraphs:


  Whereas we deemed it necessary that there should be one fold and one shepherd, for the Lord's flock in order to maintain the Christian religion in its integrity, and to confirm within us the hope of heavenly things; the unity of the Christian name was rent and well-nigh torn asunder by schisms, dissensions, heresies.


And this thought continues just a few sentences later (emphasis mine):


  Wherefore, having been, as we have said, called upon to guide and govern the bark of Peter, in so great a tempest, and in the midst of so violent an agitation of the waves of heresies, dissensions, and wars; and, not relying sufficiently on our own strength, we, first of all, cast our cares upon the Lord, that He might sustain us, and furnish our soul with firmness and strength, our understanding with prudence and wisdom. Then, recalling to mind that our predecessors, men endowed with admirable wisdom and sanctity, had often, in the extremest perils of the Christian commonwealth, had recourse to ecumenical councils and general assemblies of bishops, as the best and most opportune remedy, we also fixed our mind on holding a general council; and having consulted the opinions of those princes whose consent seemed to us to be specially useful and opportune for this our project; when we found them, at that time, not averse from so holy a work, we, as our letters and records attest, indicted an ecumenical council, and a general assembly of those bishops and other Fathers whose duty it is to assist thereat, to be opened at the city of Mantua, on the tenth of the calends of June, in the year 1537 of our Lord's Incarnation, and the third of our pontificate; having an almost assured hope that, when assembled there in the name of the Lord, He, as He promised, would be in the midst of us, and, in His goodness and mercy, easily dispel, by the breath of His mouth, all the storms and dangers of the times.


Other items were addressed, or at least were meant to be, such as reforms, but the Council was mostly held to address and condemn the practices of Protestantism.

The History Learning Site concurs:


  The Council had been called to examine doctrine and reform. Charles V had wanted abuses looked at first in an attempt to please the Protestants and hopefully tempt them back to the church. Once they were back they could look at doctrine. Paul III did not want this as reforms could financially damage him and concessions could diminish his authority.