* No-shows underscore voter mistrust of politicians
* Body will have 120 days to draft constitution
* Government struggles to assert authority over divided country
By Ulf Laessing and Ghaith Shennib
TRIPOLI, Feb 20 (Reuters) - Libyans trickled to the polls on Thursday to elect an assembly to draft a constitution, with the paltry turnout reflecting deep political disillusion with the chaos pervading Libya since Muammar Gaddafi's 42-year rule ended in 2011.
Less than 498,000 people cast ballots, the election commission said, out of one million who had registered to vote - a number far lower than the three million who did so before the 2012 parliamentary election.
Live footage from Libyan television cameras in major polling stations across the North African country showed mostly empty rooms.
Explosions rocked five polling stations at dawn in the eastern town of Derna, an Islamist stronghold, but no one was hurt.
Gunmen forced one Derna voting centre to shut by firing in the air and shouting "voting is haram (forbidden)", an election official said. Derna polling stations stayed shut and insecurity prevented some voting centres in four other towns from opening.
Nobody claimed responsibility for the Derna attacks but residents said the bombers had scrawled "There is no constitution but Islamic law" on a wall near the scene of one blast, suggesting radical Islamists were responsible.
Prime Minister Ali Zeidan's government is struggling to assert its authority over militias which helped topple Gaddafi but kept their weapons and have become major political players.
Two of the strongest militias threatened on Tuesday to dissolve the General National Congress (GNC), the interim parliament, accusing it of paralysing Libya with its endless infighting.
Libya desperately needs a viable government and system of rule so that it can focus on reconstruction and on healing the divisions exposed by the NATO-backed campaign against Gaddafi.
Soldiers guarded polling stations in the capital Tripoli, as helicopters circled overhead. In the eastern city of Benghazi, gunmen threw a bag full of explosives into a voting centre, but the devices did not go off, a security source said.
"God willing, this is the starting point for democracy and freedom, which is what we came for," Hatem al-Majri said as he voted in Benghazi.
The 60-strong constitutional committee, drawn equally from Libya's three regions of Tripolitania in the west, Cyrenaica in the east and Fezzan in the south, will have 120 days to draft the charter.
Libya used a similar model for the committee that drafted a pre-Gaddafi constitution that was implemented when the country, then a monarchy, gained independence in 1951.
The new document's authors will need to take into account political and tribal rivalries, as well as demands for more autonomy for the east, when deciding what political system Libya will adopt. Their draft will be put to a referendum.
In the east, armed protesters have occupied major oil ports since last summer to demand a greater share of energy wealth and political autonomy, crippling vital oil exports. The protest group has dismissed Thursday's vote as fake.
The election was also boycotted by the Amazigh, or Berber, minority which lives in the west near oil installations.
Its leader, Ibrahim Makhlouf, has rejected the vote because the Amazigh want a bigger say in the body and guarantees that their tongue will become one of Libya's official languages.
In the past, Amazigh have backed their demands by blockading oil installations such as the Mellitah oil and gas complex, co-owned by Italy's ENI, as well as pipelines.
Attempts to write a constitution have been delayed by political infighting in the GNC, which was elected in July 2012 for an 18-month term in Libya's first free vote in nearly 50 years.
The GNC agreed this week to hold elections this year after an outcry over its plan to extend its mandate beyond Feb. 7.
Gaddafi ostensibly ruled Libya under a bizarre set of laws prescribed in his Green Book. In practice he and his family ran a totalitarian state where no political opposition was tolerated and rival tribes were paid off or played off against each other.