Dance is an accessory to bhakti yoga and cannot be separated from bhakti. The origin of dance is mentioned in the vishNu dharmottara. Reproducing that section here.
As some parts of the text are blurred, I have indicated a few missing words with "?"+
Bharatanatyam is a shastra. Natya Shastra. It is religious by character. The stupid adage 'Art has no religion' doesn't apply to Bharatham. https://t.co/zXRMm4PTpE
— SriVaishnava Alucard (\u092a\u0930\u0915\u093e\u0932\u0930\u093e\u092e\u093e\u0928\u0941\u091c\u0926\u093e\u0938\u0928) (@BMidou124) March 30, 2022
[lakshmI, who only has eyes that see Hari, saw that God exhibiting beautiful movements of his limbs and strides of feet as he walked]+
The divine walk of bhagavAn, usually reserved for the muktAs, not seen even by gods, was manifested in front of those in bhUloka who don’t even realize what a great and rare sight that walk is!+
[lakshmI – “One who attracts the minds of all! I saw your beautiful walk as you rose up in the Ocean. Master of all! What is the vidyA behind that extreme loveliness of the walk? Tell me.”]+
[bhagavAn: Lotus eyed one! This art of dance, which is performed by graceful movements of limbs as well as the organs like eyes etc. and feet, is my body – ie, I am it’s sustainer]+
He calls nAtya as his body, ie, it is a vidyA supported by him as the self+
[bhagavAn: One who brings auspiciousness to me! Those who are my bhaktAs, will worship me with dance. The similarity to Brahman, the self of the 3 worlds is established in this dance]+
He says, dance leads to mukti as it is a limb of upAsana+
[Speaking thus to lakshmI, that supreme god told brahmA, “Knower of “dharma” – the proper means to worship me! Learn this dance, endowed with Brahman as the object & bhakti as the quality]+
[Keshava, speaking thus, taught dance to brahmA. Receiving the vidyA, brahmA gave it to rudra]
“केशवः” – Having lovely hair - implies his entire form is lovely & graceful, as origin of dance+
[Receiving this vidyA, Rudra engaged himself in constantly pleasing with dance that Ruler of Gods, Keshava, affectionate to his devotees]+
[King! vAsudeva created this dance formerly when the movables and immovables were all destroyed, ie, prior to secondary creation]+
[Since then, Shankara, the ruler of gods and who imparts knowledge of Hari to bhaktAs, worships with dance that god who bears the chakra and gada]+
“शङ्करो नृनाम्” – Who performs auspicious acts like teaching this dance to bhaktAs+
[Having obtained the name of “nR^itteshvara” (naTarAja), he ever pleases madhusUdhana. Hara is also pleased when worshipped for knowledge with dance.]+
This is indicated by his name “हर” – who “captures” madhusUdhana in his mind by bhakti.
"मधुसूधन" - who draws in the senses to his lovely form+
[Other gods are also pleased by this art of dance, which promotes the well-being of the gods (due to pleasing Hari)]+