There are nine stanzas in Datta Stavam.
All the stanzas except the last one ends with vande Smarthrugaami Sanovathu.
What is the meaning of that and what is its connection with Dattatreya?
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The complete stotra, translated into English, is available on the Hindupedia.com website.
Quoting from there:
Varadam Bhaktha Vathsalam,
Prapannarthi haram vande,
Smarthrugaami Sanovathu., 1
Salutations to Dathathreya who is a great one, Who loves and blesses his devotees, And who destroys all worries of those, Who always remember him with faith.
You can see how another stanza is translated.
Sarva Karana Kaaranaam,
Sarva Raksha karam vande,
Smarthrugaami Sanovathu., 2
Salutations to the friend of the oppressed, Who is the ocean of mercy, Who is the cause of all causes, And who protects all those, Who always remember him with faith.
Vande - Salutations (to) and Smarthrugaami Sanovathu - Who always remember him with faith.
Vande- I bow down to this revered Lord
Smaṛtṛgāmi sano’vatu- May that Lord who responds instantly when thought of!
Datta indicates gifting.
Atri and Anasuya did austerities to beget son, for the benefit of the world. The Almighty God, gifted itself to that couple in the form of a child. That is Datta. He being the son of Atri, was known as dattAtrEya.
The Almighty God resides in everyone. The concept is that the God, being the resident in everyone, need not be called loudly for response, but mere thinking of is sufficient. So the word Smaṛtṛgāmi