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feat(solvers): symplectic integrators for hamiltonian systems#85

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feat-symplectic-integrators-5023641109559256251
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feat(solvers): symplectic integrators for hamiltonian systems#85
Ryan-D-Gast wants to merge 2 commits into
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feat-symplectic-integrators-5023641109559256251

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Adds Velocity Verlet and Ruth-Forest symplectic integrators for Hamiltonian system simulations, designed to provide long-term energy preservation where standard methods (like RK4) inevitably drift. Included is an orbital mechanics example explicitly verifying the zero-drift behavior over 100 orbits.

Resolves #73


PR created automatically by Jules for task 5023641109559256251 started by @Ryan-D-Gast

Adds a `SymplecticIntegrator` numerical method generic over `S` stages, implementing standard partitioned Runge-Kutta formulations.
Included explicitly are the 2nd-order `velocity_verlet` and 4th-order `ruth_forest` constructors.
Includes a demonstration of long-term energy conservation using the Kepler problem in `examples/ode/18_orbital_mechanics_energy_conservation`.

Co-authored-by: Ryan-D-Gast <148826144+Ryan-D-Gast@users.noreply.github.com>
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feat(solvers): symplectic integrators for Hamiltonian systems

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