Python code for the solution of the three-dimensional problem of two fixed centres

The code has the following prerequisites:

• the w_elliptic library, for the computation of Weierstrass elliptic and related functions, https://github.com/bluescarni/w_elliptic,
• the mpmath library, http://mpmath.org/,
• the matplotlib/numpy stack.

Usage example:

import e3bp
e = e3bp.e3bp(1.1,1.2,1.3,[.1,.3,.4,.1,-.1,.2])

This will initialise an object e corresponding to a two fixed centres problem with the following parameters:

• a = 1.1,
• mu_1 = 1.2,
• mu_2 = 1.3,
• initial cartesian position vector [.1,.3,.4],
• initial cartesian velocity vector [.1,-.1,.2].

The e object can then be used as follows:

e.xi_tau(0.1) # Compute the xi coordinate at tau = 0.1
e.eta_tau(0.2) # Compute the eta coordinate at tau = 0.2
e.ell_ham_state_tau(0.3) # Compute the Hamiltonian state at tau = 0.3