I understand why the Carolingian Empire collapsed, but how exactly did a powerful and famous dynasty come to lose power over much smaller and easier to manage domains? In both kingdoms, nobles simply stopped respecting dynastic succession and elected their own successors to the kingship. To me this seems to display the lack of power the dynasty had in the 10th century, and I'm wondering how it was weakened to this point.
HI,
The two basic problem with the Carolingian empire was twofold its size and poor administrative capability and the Frankish inheritance system. Despite the growth of a unitary central court for the Frankish realm under Charlemagne and some attempts to expand direct rule and policy via the missi dominici the empire was actually very decentralized, with rule by the local nobility (many viewed as sub-monarchies). Charlemange, his forebears and heirs had to put down repeated revolts and re-assert authority on parts of their empire. Today, the extent of the Empire may seem small but given the poor roads, a patchwork of landed authorities (princelings, duchies, monastaries/ecclastical estates) with no real bureaucracy and rule by fiat; it was difficult to govern.
Secondly, why was the empire so fragmented in the first place. Frankish (and by extension most early medieval states) inheritance laws did not use primogeniture. At death, the estate of the deceased was partitioned between family members depending on the will, or simply semi equitably. This included not only the sons of the deceased, but in some cases brothers and uncles and even sons-in-law. This lead to both fragmentation of the realm administratively , economically and politically. Each would be considered a princely domain and often had its own court, policy, and even war host and saw each other as equal, and even as rivals. The "emperor" was powerful, but only as far as his own estate allowed him to be, at times could simply be viewed the first among equals. This was not only a problem at the highest level but smallholders increasingly were also fragmanted that some estates became unviable and scattered over generations.
Indeed, fratricidal wars among Frankish heirs were common. The treaty of Verdun (843) which split the Empire into East and West Francia and Lotharingia was the result of the wars over the sons of Louis the Pious. Despite the consolidation of power by the later Ottonian Emperors the HRE ( aka East Francia) continued to internally fragment and by the renaissance it came to be a complete political mess. France (west Francia) was also a in reality more of a collection of appenages under the nominal suzerainty of a weak king in Paris for most of the medieval era.
I hope that very brief answer helps you.