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WorkOS
The modern identity platform for B2B SaaS. The APIs are flexible and easy-to-use, supporting authentication, user identity, and complex enterprise features like SSO and SCIM provisioning.
MERCURY is a classic N body integrator
It depends what you want to do. If you just want to write a "toy" simulation from scratch for learning purposes, then you don't really need any libraries, except maybe something to visualise/animate the simulation output. For C++, if you don't mind being limited to 2D SFML is very easy to get started with.
NOTE:
The number of mentions on this list indicates mentions on common posts plus user suggested alternatives.
Hence, a higher number means a more popular project.