- Symplectic integrators are numerical schemes that solve first-order differential equations for Hamiltonian systems; thus, they can be used in [nonlinear dynamics](https://en.wikipedia.org/wiki/Nonlinear_dynamics "Nonlinear dynamics"), [molecular dynamics](https://en.wikipedia.org/wiki/Molecular_dynamics "Molecular dynamics"), and [celestial mechanics](https://en.wikipedia.org/wiki/Celestial_mechanics "Celestial mechanics"). - Variational integrators are integrators derived using Lagrangian mechanics, which you can see in notes under [[5 Contact Dynamics in Autonomous Robotic Systems|note topic 5]]- derivations are also being developed under there. -