adding libration point calculation using newton raphson method

[DhruvJ22]

I like my method of libration point calculation compared to the one in restricted.py that uses brentq:

1. Compatible with cr3bp_char_quant
2. Uses non-dim units, which will be helpful later for cr3bp propagation
3. Uses Newton Raphson instead of brentq as I am not sure if the limit intervals set for brentq can encapsulate all systems, while Newton Raphson is more robust
4. Uses regularized form of the CR3BP EOMs to define a function, whose zeros are the liberation points -> less susceptible numerical errors

a. The function and its test work if I compare their values but L_ND is throwing an error that I am having difficulty getting around. I have tried to use 'u_enabled_units' but that has not resolved the problem.
b. I would like to add the L_ND and V_ND (added as comments in SystemChars) so that we can use SystemChars' object and not have to define the units in multiple functions.

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📚 Documentation preview 📚: https://poliastro--1573.org.readthedocs.build/en/1573/

[DhruvJ22]

Note to self: need to add T_ND: non-dim unit for time

[astrojuanlu]

Hi @DhruvJ22, sorry for the huge delay 🙏🏽

I have one very high level comment: if I understand correctly, newton_raphson_lib_calc finds the root of a power series polynomial. However, if I understand correctly, finding the roots of a polynomial does not require a numerical solver, and can be done with a highly efficient linear algebra method:

https://mathworld.wolfram.com/PolynomialRoots.html

In fact, this method is available in NumPy:

https://numpy.org/doc/stable/reference/generated/numpy.polynomial.polynomial.Polynomial.roots.html

as demonstrated here:

In [1]: import numpy as np

In [2]: p = np.polynomial.Polynomial([1, 2, -3])

In [3]: p
Out[3]: Polynomial([ 1.,  2., -3.], domain=[-1,  1], window=[-1,  1])

In [4]: p.roots()
Out[4]: array([-0.33333333,  1.        ])

Therefore, could you please

1. Remove the Newton-Raphson implementation and rewrite everything in terms of NumPy polynomials instead, and
2. Uncomment the problematic unit definitions, so that your tests fail and I can see what exactly the problem is?

[DhruvJ22]

Adding a note to my previous PR that I forgot to convey publicly: the problematic unit definitions are uncommented and the code should give an error as is.