Guiding Center 4d Deeply Passing with Symmetric SRK3 VPRK Method and Projections
The time step and number of time steps are those of this orbit, set in src/guiding-center-4d.jl; the toroidal momentum is shown alongside the energy, as the second invariant of the guiding centre dynamics.
SymplecticSRK3

SymplecticSRK3 with standard projection

SymplecticSRK3 with symmetric projection

SymplecticSRK3 with symplectic projection

SymplecticSRK3 with midpoint projection

SymplecticSRK3 with internal stage projection
Simulation crashed after 0 of 12500 time steps: MethodError.