I am a Gayatri upasak and a proud desciple of Vedmurty, taponistha Pt.Shriram Sharma Acharyaji, the founder of All world Gayatri Pariwar. According to his literature, one of the interpretation of Gayatri as Tripada is as follows;
The gayatri mantra has three charans in it;
1. Om Bhur bhuvah swah - Bhakti yoga
Om - Pranav, the name of God
Bhu, bhuvah and swah - Akash, patal and pruthvi
This part of Gayatri mantra makes you belive that the God is in all three places
2. tat savitu varenyam bhargo devasya dheemahi - Gnyan yoga
tat - that - the God
savitu - illuminous like sun
varenyam - the best
bhargo - who destrys our sins
devasya - devine
dheemahi - we have
This part of Gayatri mantra gives you the highest knowledge that, we are having the qualities of God.
3. Dhiyo yonah prachodayat - Karma yoga
Dhiyo - intellect
yonah - righteous path
prachodayat - takes forcefully
Take our intellect to a righteous path forcefully
Once your intellect becomes righteous, you do do everything as your duty without expecting the fruit of actions.
Gayatri is the Yug Shakti today. Righteous intellect is the requirement of this age.