Theory

Mathematical background for the package. Each document below is a standalone derivation; the Quick Start and Internals pages cover the practical API counterpart.

Core Theory

• Weber Electrodynamics — potential, force law, Lagrangian, Hamiltonian, and equations of motion in Gauss–Weber units
• Semi-Explicit Symplectic Integrator — extended phase space, Strang splitting, symmetric projection via Lagrange multipliers (Jayawardana & Ohsawa 2021)
• Initial Conditions — constructing valid q0/p0 for target orbits: two-body, symmetric N-body polygon, 3D rigid rotation, and Zöllner case; circular velocity, η_v velocity scale, energy–angular-momentum parameterisation
• Regularization — Levi-Civita (2D) and KS (3D) coordinate transforms; mathematical derivations of the fictitious-time integration
• Regularization Design — backend semantics, encounter dispatch, hysteresis, lifted-pair and adaptive-Cartesian step design, chain mode

Zöllner Extension

• Zöllner Electrogravitational Theory — κ mismatch derivation, emergent gravitational attraction from electrical dyads, comparison with Newtonian gravity