System

WeberSystem

Symbolic and compiled representation of the n-body Weber Hamiltonian.

Constructed once for a given (n_particles, dims) pair via WeberSystem(n_particles, dims). The compiled equations of motion are reused across many WeberProblem instances with different physical parameters. Construction involves symbolic differentiation and code generation via Symbolics.jl; expect a few seconds for the first call.

Fields

• n_particles::Int: Number of charged particles.
• dims::Int: Spatial dimension (1, 2, or 3).
• q_symbols::Vector{Num}: Symbolic coordinate variables [x1, y1, ..., xN, yN, ...].
• p_symbols::Vector{Num}: Symbolic momentum variables [px1, py1, ...].
• param_symbols: Symbolic parameter vector [m1…mN, q1…qN, c, κ12, κ13, …].
• hamiltonian_symbolic: Full symbolic Weber Hamiltonian expression.
• dq_dt_symbolic, dp_dt_symbolic: Symbolic Hamilton's equations.
• dq_dt_compiled, dp_dt_compiled: In-place compiled equations of motion.
• hamiltonian_compiled: Compiled scalar Hamiltonian function.
• degrees_of_freedom::Int: Total DOF = n_particles × dims.

WeberSystem(n_particles::Int, dims::Int) -> WeberSystem

Build and compile the symbolic Weber Hamiltonian for n_particles particles in dims dimensions.

Uses Symbolics.jl to derive Hamilton's equations analytically, then compiles them to efficient in-place Julia functions via build_function. The resulting WeberSystem can be reused across multiple WeberProblem instances.

Arguments

• n_particles: Number of particles (≥ 1).
• dims: Spatial dimension; must be 1, 2, or 3.

Returns

• WeberSystem with compiled equations of motion ready for WeberProblem.