Who is satyaki and why he fought on the side of the Pandavas in Kurukshetra war?
Satyaki spared Karna's life in Kurukshetra war for Arjuna's vow, is it true? I think not even arjuna defeated Karna in a straight battle (with out Krishna).
Satyaki also known as Yuyudhāna was son of the King Satyaka & grandson of Sini. He was from Satvata -Vamsha he learnt the science of archery from Arjuna. He was Athiratha warrior.
रौक्मणेयश्च साम्बश्च युयुधानश्च सात्यकि : |
सुधर्मा चानिरुद्भश्च शैबस्च नरपुण्ड:व: || MB 2.4||
P. 7 - Yuyudhana the son of Satyaki and Sudharman and Aniruddha and Saivya that foremost of men who had learnt the science of arms under Arjuna these and many other kings.
The two sons of Nighna were Satrajita and Prasena. Another son of Anamitra was another Sini, and his son was Satyaka.The son of Satyaka was Yuyudhana, whose son was Jaya. From Jaya came a son named Kuni and from Kuni a son named Yugandhara. Another son of Anamitra was Vrsni.
Satyaki was partial incarnation of Maruts , he was also committed to truthfulness .
सात्यकि: सत्यसन्धच्य योSसौ वृष्णिकुलोद्वह : |
पक्षात् स जज्ञ्ने मरुतां देवानामरिमर्दन: | | MB 1.67 ||
P. 142 - And he who was Satyaki of sure aim, that upholder of the pride of Vrishni race, that oppressor of foes, begotten of the portion of gods called the Maruts.
तत: सात्यकिमारोप्य प्रययौ पुरुषोत्तम: |
पृथिवीं चान्तरिक्षं च रथघोषेण नादयन || MB 5.83 ||
P. 172 -And taking Satyaki also upon it, that best of male beings set out, filling the earth and the welkin with the rattle of his chariot-wheels. And the sky became cloudless, and auspicious winds began to blow around, and the atmosphere freed from the dust became pure.
युयुधानस्ततो वीर : सात्वतानां महारथ : |
महता चतुरङ्गेण बलेनागाद युधिष्ठिरम || MB 5.19||
Vaisampayana said, 'Then Yuyudhana, the great hero of the Satwata race, came to Yudhishthira with a large army of foot, and horses and cars and elephants. And his soldiers of great valour come from various lands, bore various weapons of war, and heroic in look they beautified the Pandava army. And that army looked splendid by reason of battleaxes, and missiles and spears, and lances, and mallets, and clubs, and staves, and cords, and stainless swords, and daggers, and arrows of various kinds, all of the best temper. And the army, beautified by those weapons, and resembling in colour the cloudy sky, assumed an appearance like to amass of clouds with lightning-flashes in its midst
अक्षोहिणी तु सा सेना तदा यौधिष्ठिरं बलं |
प्रविश्यान्तर्दधे राजन् सागरं कुनदी यथा : ||MB 5.19 ||
And the army counted an Akshauhini of troops. And when absorbed in the troops of Yudhishthira it entirely disappeared, as doth a small river when it enters the sea.
He was aware of minds of Duryodhana and his confidants , when they planned to capture Krishna, the messenger, as a prisoner; he advised Kritavarma to rally the troops outside the court, and informed Krishna, Dhritarashtra & Vidura about the Kauravas.
तेषां पपमभिप्रायं पापानां दृष्ट चेतसाम |
इङ्गितज्ञ: कवि : क्षिप्रमन्वबुद्भ्यत सात्यकि : || MB 5.130 ||
After those sinful men of wicked souls had come to this sinful resolution, highly intelligent Satyaki, capable of reading the heart by signs, soon came to know of it. And because of that knowledge, he soon issued out of the court, accompanied by Hridika's son (Kritavarman). And Satyaki addressed Kritavarman, saying, 'Array the troops soon. And accoutred in mail and with thy troops arrayed for battle
After the Kurukshetra war,Yadavas retired to Prabhasa . There all drank wine and started quarrelling , in that all the warriors of Andhaka Clan killed him upon seeing that Satyaki killed Kritavarma.
बहुत्वान निहतौ तत्र उभौ कृष्णस्य पश्यतः |
हतं दृष्ट्वा तु शैनेयं पुत्रं च यदुनन्दनः ||
एरकाणां तदा मुष्टिं कॊपाज जग्राह केशवः |
Having said these words, Satyaki rushed at Kritavarma and severed his head with a sword in the very sight of Keshava. Yuyudhana, having achieved this feat, began to strike down others there present. Hrishikesa ran to prevent him from doing further mischief. At that time, however, O monarch, the Bhojas and Andhakas, impelled by the perverseness of the hour that had come upon them, all became as one man and surrounded the son of Sini. Janardana of mighty energy, knowing the character of the hour, stood unmoved without giving way to anger at the sight of those heroes rushing in wrath at Satyaki from every side. Urged by fate and inebriated with drink, they began to strike Yuyudhana with the pots from which they had been eating. When the son of Sini was being thus assaulted, Rukmini’s son became highly enraged. Book 16: Mausala Parva-SECTION 3
Even though Krishna offered his Narayani sena and gopas to Kauravas , Satyaki decided to fight on the side of Pandavas because he was aware of the wickedness of the Kauravas as he was mind reader , and already saw that when Kauravas were planing to arrest Krishna ,even he was peace messanger ,he was extreme follower of truthfulness . So probably disliking wicked and untruthful acts of Kauravas he decided to be on the side on Pandavas. Also he was relative of Pandavas ,although he was from Satvata Vamsha and was residing in Dwaraka as described in the below verse. Satyaki strongly and passionately favored the cause of the Pandavas. He also defended Dwaraka of Krishna when King of Salwa attacked the city. And as he was residing in Dwarka and closely associated with Krishna , as Krishna took the side of Pandavas , he also joined them. Also one of the reasons could be that Arjuna was his Guru , and inspite of taking side of Adharma he chosen side of Dharma.
कच्चिदानर्तपुर्यां नः स्वजनाः सुखमासते ।
मधुभोजदशार्हार्ह सात्वतान्धकवृष्णयः ॥ SB 1.14.25 ॥
kaccid ānarta-puryāḿ naḥ sva-janāḥ sukham āsate
Maharaja Yudhisṭhira said: My dear brother, please tell me whether our friends and relatives, such as Madhu, Bhoja, Dasarha, Ārha, Satvata, Andhaka and the members of the Yadu family are all passing their days in happiness.