While the other leaders offered brief handshakes and stiff smiles, India's Prime Minister strode out of the wings to greet his Australian counterpart with an exuberant hug.

You got the same sense about Modi when he was later mobbed by chanting fans at the unveiling of a statue in Brisbane and then tweeted about how touched he was. And again when thousands of Indian Australians spent a whole day dancing, drumming and partying in anticipation of his speech in Sydney.

But when Modi began to address the Parliament in Canberra on Tuesday, we knew there was something about the Indian Prime Minister.

It wasn't just that he acknowledged indigenous Australians when Abbott did not in his introductory remarks.

Or that he wondered how MPs were surviving a third address to Parliament by a world leader in as many days.

"Maybe this is Prime Minister Abbott's way of shirt-fronting you," he suggested with the hint of a wink.

It wasn't even the fact that – although he had an autocue – he appeared not to be speaking from prepared notes. He was eyes up all the way through.

It was because as soon as Modi got stuck into the substance of his address, he had the normally rowdy House hypnotised.

"I come to you with the greetings of 1.25 billion people … and today I have come to unite in spirit, as we once were in geography," he declared.

In cadences befitting of someone who is a published poet as well as a politician, Modi spoke of how democracy offers "the best opportunity for the human spirit to flourish" and loaded praise on Australia, whose cities are "alive with [the] richness of this world's diversity".

But his stylish words also carried a serious message: India is open for business.

There are 800 million Indians under the age of 35, "eager for change, willing to work for it because, now they believe that it is possible".

Young Indians want energy that "does not cause our glaciers to melt", cities that are "smart, sustainable and liveable" and villages that "offer opportunity". And they want Australia's help to get there.

"India will be the answer to your search for new economic opportunities ... your source for world-class skills at home or for a manufacturing location abroad," he said with all the polish and confidence of a new car salesman.

As he concluded with a simple "thanks a lot", the chamber rose in a standing ovation.

They were not just being polite. If Madam Speaker had let them, they would have whistled, whooped and charged the stage.

That's what you do when you see a rock star perform.