Lord Shiva had 2 bows - Pinaka and Ajagava. There are few stories associated with the first bow Pinaka like Sita swayamvar.
Are there any distinct stories/incidents associated with Ajagava that have been mentioned in our scriptures for instance Shiva Puran or any other purans?
Significance of Rudrakshas:
Maha Deva was tired in tracking the tricky and invincible Demon Tripurasura, finally pulled out his ‘Ajagava’ dhanush and despatched the unique Vikaaraal arrow and killed him. The long chase of the Asura who was fortified with Brahma’s boons tired out Maheswara and this tedious task ended up with profuse tears from his right eye signifying Surya Netra and from the streams thus materialised emerged Rudraksha Trees yielded twenty kinds of yellow seeds, while from his left eye called Soma Netra came sixteen varieties of white coloured beads and from the third eye on the forehead called Agni Netra came black beads.
Source - The book "PURANA SARAAMSHA (Quintessence of Puranas)"
According to this book, the story of Lord Shiva killing Tripurasura using the Ajagava bow is found in Padma Purana, Devi Bhagavatam, Shiva Purana and Skanda Purana.
(Source: Padma Purana, Devi Bhagavata, Siva Purana, Skanda Purana etc.)
According to Matsya Purana, Agajava was used again by Lord Shiva during the battle that ensued as a result of Chandra abducting Brihaspati's wife Tara.
Quoting from the book "Essence of Matsya Purana":
In course of time, Chandra got infatuated with Devi Tara, the wife Deva Guru Brihaspati and took her away to his residence despite heavy protests of Deva Guru, Sadhyagana, Lokapalakas, Marudganas, and even Bhagavan Shiva himself. Shiva felt highly offended and invoked the Ekadasha Rudras led by Vamadeva, pulled out his bow called ‘Ajagava’, and accompanied by eighty four Ganas, Ganesha, Kubera with his shata koti Yakshas, Padma Vetala, three lakh Nagas and twelve lakh Kinnaras and so on. Chandra on his part too elisted the support of Nakshatras, Rakshasas, Asuras, Daityas, Shanishwara, Mangala, and so on.
However, according to the writings of this blog, Ajagava is nothing but the Pinaka bow (and I agree with this view).
Rudra is described as fierce; armed with the mighty bow (pinaka), and a quiver holding unending array of arrows and missiles which are terrifyingly swift and penetrating. His fast-flying arrows, ‘brilliant shafts run about the heaven and the earth’ (RV 7.46.3).
Pinaka the powerful, sturdy bow with a wide span, bending along the course of the Sun , is said to be the symbol of Rudra, the Isana (Lord); and, his supremacy over all others. In the later texts, Pinaka is also known as Ajagava, the southern part of the Sun’s path. (Ajagava is also explained as a bow made of the horns of goats.)
Oh, the devoted to the devotees, always travelling in the chariot, ever young, fierce like the lion, vanquisher of the enemies, May the devotees pray to you. May you make us happy. May your armies fight against the enemies and be merciful towards us. There is none that matches him in strength. He is the Ishana the Master of the world; he is the father of worlds (Bhuvanasya pitaram).He commands men and entrusts tasks. He sets things in motion and makes flow like a river. He is medhavi, intelligent and the compassionate one. He is praised as midvah, for his generosity. As he is an auspicious one, he is called Shiva. (RV: 2-33-7; 6-49-10; 7-46-2)
Note: As per Mahabharata, the king Prithu (from whom the earth got it's name Prithivi) also used to own a bow called Ajagava.
The very mountains used to yield him openings that he might pass through them. The standard of his car never broke (obstructed by anything). Once on a time, the tall trees of the forest, the mountains, the gods, the Asuras, men, the snakes, the seven Rishis, the Apsaras, and the Pitris, all came to Prithu, seated at his ease, and addressing him, said, ‘Thou art our Emperor. Thou art our king. Thou art our protector and Father.
Thou art our Lord. Therefore, O great king, give us boons after our own hearts, through which we may, for ever, obtain gratification and joy.’ Unto them Prithu, the son of Vena, said, So be it. Then taking up his Ajagava bow[117] and some terrible arrows the like of which existed not, he reflected for a moment.
There was a mention of Ājagava in Viṣṇu Purāṇa | Book 1 - Chapter 13.
Sages eliminated King Vena, who reviled Yagna (the god of sacrifice) and thus was not fit to reign over the earth.
As the kingdom is without a king, the dishonest men have begun to seize the property of their neighbours.
The sages, hearing this, consulted, and together rubbed the the right arm of the king, who had left no offspring, to produce a son. From which friction was engendered the illustrious son of Veṇa, named Prithu, resplendent in person, as if the blazing deity of Fire bad been manifested.
There then fell from the sky the primitive bow (of Mahādeva) named Ājagava, and celestial arrows, and panoply from heaven.
The story continued, as follows:
Protecting this earth, the monarch performed many great sacrificial ceremonies, accompanied by liberal donations.
His subjects soon approached him, suffering from the famine by which they were afflicted, as all the edible plants had perished during the season of anarchy.
In reply to his question of the cause of their coming, they told him, that in the interval in which the earth was without a king all vegetable products had been withheld, and that consequently the people had perished.
"Thou," said they, "art the bestower of subsistence to us; thou art appointed, by the creator, the protector of the people: grant us vegetables, the support of the lives of thy subjects, who are perishing with hunger."
On hearing this, Prithu took up his divine bow Ājagava, and his celestial arrows, and in great wrath marched forth to assail the Earth.
Earth, assuming the figure of a cow, fled hastily from him, and traversed, through fear of the king, the regions of Brahmā and the heavenly spheres; but wherever went the supporter of living things, there she beheld Vaiṇya with uplifted weapons:
