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Are there equations to describe the Symplectic Euler?


Can the difference between forward Euler and symplectic Euler be understood the following way: Forward Euler explicitly calculates the velocity at current configuration whereas symplectic Euler accumulates changes in velocity at each configuration?


Can we assume that the "almost exactly" part of the energy conservation is energy loss (damping) and not energy gain, like forward Euler? In other words, over a long time, would the pendulum stop or go out of control?


Symplectic looks kind of complex to me, and I agree with the difference mentioned by outousan.


What do the equations look like to describe this?