Poland-Lithuania was only even vaguely hegemonic and militarily protagonistic for slightly over half of that period.
Still, that was as good as it got.
It all started in the 1640s with failure of the planned war against the Ottomans - the main goal of which was to conquer the Crimean Khanate. Also a coup d'etat was planned (with use of forces gathered for this war, after its successful end), the goal of which was to limit the extent of noble democracy and privileges. The main actors of that game were king Wladyslaw IV Vasa (he was by far the best of Polish kings in 17th century), hetman Stanislaw Koniecpolski and chancellor Jerzy Ossolinski. Koniecpolski died in 1646, king Wladyslaw's unfortunate death - due to an overdose of laxatives - was in 1648. Ossolinski died in 1650. So things didn't go well. In 1648 a major Cossack Uprising under Bohdan Khmelnytsky started - after the death of their favourite king (he was very respected by Cossacks, because he made extensive use of Cossack soldiers in his military campaigns, giving them the opportunity to fight and get rich - something they liked most) and the subsequent final failure of the planned grand expedition against the Ottomans. The moment of weakness and chaos of the Polish-Lithuanian Commonwealth was then exploited by nearly all of her neighbours- and so the series of disastrous wars continued until 1667. In 1655 Sweden backstabbed PLC from behind. Actually Charles X Gustav was popular among Polish nobility, many of whom would like to see him on the Polish throne instead of John Casimir - who was generally considered as an inept king. This is why so many Lithuanians and Poles betrayed to the Swedish camp. They came back only when they realized what was the Swedish policy in captured territories. PLC in the end came out on top from all of these wars in years 1648 - 1667, but the state's economy was in ruins. Material losses were great.
It was not the crisis of Polish-Lithuanian way of warfare, however, which caused these problems.
For example initial defeats against Sweden in 1655 were caused by fact that PLC's army which was mobilized to face the Swedes in 1655 was much weaker than PLC's armies which fought against Sweden in previous wars - those in years 1601 - 1629. It was strong on paper when it comes to numbers, but quality and composition of this army in 1655 was much worse than quality of armies which fought in previous wars vs Sweden.
There was also problem with espirit de corps - many citizens would like to see Charles X on the Polish throne rather than John Casimir.
And also commanders of Polish-Lithuanian armies at that time were not as skilled as during previous wars against Sweden. One of the best commanders of PLC's armies at that time - Janusz Radziwill (who for example won against Russians and Cossacks in the battle of Szklow on 12 August 1654, where his forces were outnumbered) betrayed to the Swedish side, signing the Treaty of Kiejdany with Charles X Gustav. Regarding composition:
We should compare the composition and quality of army which faced the Swedish invasion in 1655 especially with the composition and quality of Polish army mobilized for war against Sweden in 1635 (this war in the end did not take place - that's why some historians call it "armed demonstration against Sweden" - but it didn't take place because Sweden agreed to sign the favourable for Poland Treaty of Stuhmsdorf on 12 September 1635).
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Regular Polish (Crown) army mobilized for planned war against Sweden in 1635:
- 4060 hussars (17%)
- 4890 "cossack" cavalry (20%)
- 620 reiters & 1900 dragoons (10%)
- 12,700 infantry (53%)
Total regulars: 24,170 regular Crown army. Add to this 3630 regular soldiers of the quarter army and from Lithuania, as well as ca. 7,000 registery Cossacks. In total around 35,000 soldiers - including 28,000 regulars and 7.000 registery Cossacks.
And this was the perfect army composition for war against Sweden, based on experiences from previous wars.
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By comparison in 1655 Poland deployed:
Against Sweden:
Regular army (in brackets - % of total regulars):
- 700 hussars (7%)
- 6340 other cavalry (light & medium) and dragoons (62%)
- 3150 infantry (31%)
In total 10,200. As you can see, not only it was a small force of regulars, but also had not enough infantry (just 31%) and heavy cavalry (just 7%).
Add to this:
- 5300 voivode and private forces (1650 cavalry and 3650 infantry)
- 4300 levy peasant infantry (so called chosen infantry or łan's infantry)
- 32,000 nobles from
Levée en masse
Total of 51,800 - but 70% of this were troops of very low combat value (32,000 + 4300) and further 10% (5300) troops of often dubious loyalty.
Of those 32,000 noble levies many would like to see Charles X on the Polish-Lithuanian throne more than John Casimir.
13,000 of those 32,000 noble levies (so over 40%) surrendered at Ujscie on 25 July 1655
without a single shot.
Against Russian-Cossack alliance:
Regular Crown army - 9400
Regular Lithuanian army - ca. 10,000 (partially betrayed to the Swedes after the Treaty of Kiejdany)
Łan's infantry - 300
Noble levies - 4000
And also 15,000 Crimean Tatars, who previously had been supporting Cossacks but now fought on the Polish side vs Russo-Cossack alliance.
As you can see, actually much more (19,400 compared to 10,200) regulars fought vs the Russian-Cossack alliance than vs Sweden.
But Russian-Cossack army operating against PLC in 1655 was massive - much bigger than Swedish army.
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And Swedish forces at the beginning were 34,000 regular army (12,950 cavalry, 1200 dragoons and 19,800 infantry), shortly later they grew to 42,000 regulars at the start of August, then to 55,000 regulars - and by the end of the year (1655) they amounted 68,000 regulars, despite already large losses.
These are just Swedish regulars. Add to this all other forces - Swedish allies and Lithuanians and Poles who joined Swedish side.