.. _miscellaneous:

Miscellaneous
=============

A number of useful odds and ends are gathered into the :mod:`celmech.miscellaneous` module.
These include:

1. **Frequency analysis**: 
The :func:`~celmech.miscellaneous.frequency_modified_fourier_transform` function
provides a wrapper for the FMFT algorithm of `Šidlichovský & Nesvorný (1996)`_. 
A jupyter notebook example is available `here`_.

2. **AMD**: Functions related to angular momentum deficit (AMD) and 
the analytic stability criteria (see `Laskar & Petit (2017)`_): 

   - :func:`~celmech.miscellaneous.compute_AMD`
   
   - :func:`~celmech.miscellaneous.AMD_stable_Q`
   
   - :func:`~celmech.miscellaneous.AMD_stability_coefficients`
   
   - :func:`~celmech.miscellaneous.critical_relative_AMD`

   - :func:`~celmech.miscellaneous.critical_relative_AMD_resonance_overlap`

3. The function :func:`~celmech.miscellaneous.holman_weigert_stability_boundary` 
   which computes a stability criterion for circum-binary planets based on `Holman & Wiegert (1999)`_

4. The functions :func:`~celmech.miscellaneous.sk` and :func:`~celmech.miscellaneous.Dsk`
   which give approximate disturbing function coefficient amplitudes as and their derivatives
   with respect to eccentricity. 
   See `Hadden & Lithwick (2018) <https://ui.adsabs.harvard.edu/abs/2018AJ....156...95H/abstract>`_

5. Convenience functions :func:`~celmech.miscellaneous.get_symbol` and :func:`~celmech.miscellaneous.get_symbol0` for generating sympy symbols from LaTeX strings.

6. The function :func:`~celmech.miscellaneous.truncated_expansion` for expanding and
   truncating sympy expressions after assigning variables (possibly different) orders
   in a book-keeping parameter.


.. _here: https://github.com/shadden/celmech/blob/style_update/jupyter_examples/FrequencyAnalysis.ipynb
.. _Laskar & Petit (2017): https://ui.adsabs.harvard.edu/abs/2017A%26A...605A..72L/abstract
.. _Holman & Wiegert (1999): https://ui.adsabs.harvard.edu/abs/1999AJ....117..621H/abstract


API
---

.. automodule:: celmech.miscellaneous
    :members:

.. _SimulationArchive: https://github.com/hannorein/rebound/blob/main/ipython_examples/SimulationArchive.ipynb