EoMs.jl

__precompile__()
module EoMs

    # This module contains the Equations of motion
    # of PPN two-body problem
    # Note: I assume G = c = 1

    export EoM_massless

    function EoM_massless(u, p, t)

        x, y, vx, vy = u
        M, β, γ = p

        r = √(x^2 + y^2)
        φ = -M / r
        v² = vx^2 + vy^2
        rv = x * vx + y * vy

        A = - (1 + 2 * (β + γ) * φ + γ * v²) * M / r^3
        B = M * (2 * γ + 2) * rv / r^3

        acc_x = A * x + B * vx
        acc_y = A * y + B * vy

        return [vx, vy, acc_x, acc_y]

    end

    function EoM_general(u, p, t)

        x1, y1, vx1, vy1, x2, y2, vx2, vy2 = u
        M1, M2, β, γ = p

    end

end