# Symplectic integrator

## Numerical integration scheme for Hamiltonian systems / From Wikipedia, the free encyclopedia

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In mathematics, a **symplectic integrator (SI)** is a numerical integration scheme for Hamiltonian systems. Symplectic integrators form the subclass of geometric integrators which, by definition, are canonical transformations. They are widely used in nonlinear dynamics, molecular dynamics, discrete element methods, accelerator physics, plasma physics, quantum physics, and celestial mechanics.