unlisted
ubuntu2404a
�6i�4 � @ s d Z ddlZddlZe�d�Zejddd�Zejddd�Ze�d�Z d d
� Z
ded ded
d ed
e
e� e
e� e de dd
ed
d
Zed e
e�eee
e� d de dd
ed
d
Zed
ed
e
e� e
e� e de dd
ed
d
Z
e
Ze
d
ZeZded ded
d
ed
d e
e� e de dd
ed
d
Zeed e ed d e
e� ddd
ed
d
Zeed
Ze ed
Zed
ded ded ded ded ded ded
d ded
ded ded d ed d!ed
d ed e
e�d d"e d#ed d$ed d%ed d&ed d'ed d(ed
d) ed e
e�d ed*ed d+ed d,ed d-ed d.ed d/ed d0ed
d1 e
e� dd2ed! d3ed d4ed d5ed d6ed d7ed d8ed d9ed
d: e
e�d
d;ed
d<d
ed
d d=ed
ded
e e
e� d
d=ed de ded e
e� ded
d e
e� de d< Zed
d>ed" d?ed d@ed dAed de d"ed ed
d ed
e
e�d ded d"ed ded dBed
d e e
e�d
ded dCed dDed dEed dFed
d e
e� ded
ed d
d=ed
ded
e e
e� d
d=ed de ded e
e� d< Zed
dGed dHed dIed dJed dKed
dL ded
ded ed ded
d ed e
e�d d"e ded dMed dNed dOed dPed
d ed e
e�d dQedR dSedT dUed" dVed dWed dXed dYe e
e� ddZed dGed d[ed d\ed d]ed d^ed d_ed
d` e
e�d
d;ed
d<d
ed
d d=ed
ded
e e
e� d
d=ed de ded e
e� ded
d e
e� de d< ZeZe da Ze da Zed
dbed dced dded deed dfed
dg d"ed
d"ed ded
d
ed e
e�d de dhed died djed dked dled
dm ed e
e�d dnedR doedT dped" dqed dred dsed dte e
e� dued dved dwed dxed dyed dzed d{ed
d| e
e�d
ded
ed d
d=ed
ded
e e
e� d
d=ed de ded e
e� ded
d e
e� de d< Zed
ded d}ed d~ed ded dDed
d| d"ed ded d
ed
d ed e
e�d de dted d�ed d�ed djed d�ed
d ed e
e�d edhed d�ed d�ed d�ed d@ed d)ed
d e
e� d�ed d�ed d�ed d�ed d�ed d�ed d�ed
d e
e�d
ded
ed d
d=ed
ded
e e
e� d
d=ed de ded e
e� ded
d e
e� de d< Zed
dGed dHed dIed dJed dKed
dL ded
ded ed ded
d ed e
e�d d"e ded dMed dNed dOed dPed
d ed e
e�d dQedR dSedT dUed" dVed dWed dXed dYe e
e� ddZed dGed d[ed d\ed d]ed d^ed d_ed
d` e
e�d
d�ed
d
ed
d d d=ed
ded
e e
e� d
d=ed de ded e
e� ded
d e
e� de d< Ze Zd
ej Z d
ej ed ed d< Z!d
ej d
e d
d e d
ed
d d� d Z"d
ej ed d
ed d� Z#dej d
ed
de�$e d
d e d
ed
d � de d
d de e�$e d
d e d
ed
d � e�$e d
d e d
ed
d � dde d
d ed e�$e d
d e d
ed
d � ed e�$e d
d e d
ed
d �d!e d e d
d
d
ed
d d
e�$e d
d e d
ed
d � d< Z%ejed
d ed d� Z&ej d�e d
d e d
ed
d d� e d
ed d
d e d� ed
d d< Z'ejed d
ed d� Z(ej ed
d de d ed e d
ed d ded
e�$e d
d e d
ed
d � ded
d e�$e d
d e d
ed
d �d e d� ed
d d= Z)d�d�� Z*d�d�� Z+d�d�� Z,d�d�d��Z-dS )�z�
Created on Fri Nov 7 18:39:55 2025
@author: davide
Methods that calculates the orbit variation delta_C for an oblate particle given its aspect ratio
� Nz\kappa�xiT)Zpositivez
\overline{xi}�Cc C s dt �| d | d � S )N� �?� )�sym�log)�val� r �\/Users/davide/Downloads/Joint_paper_figures/jupyter_notebook_submission/figure_5/Dabade16.py�invcoth s r � � � � � r �( � ix���� iF �
i� � iA. � i5$ i� � � � � � � i i4 � i i� i � i
il il6 i�R i�7 iA i�
i� i i� i� i� i� i� i�
iQ �: i� ����������i����� �s �Z � �W � �! �4 iz i! i{ i� iA iV � �� i � i4����
iD � i� i�( i iO �, �� �m i� i� i i7 � g @�Q i� i2 i� i� �6 �l �� �E � � � i����i i� i= i� �O �$ i� i� i� i
�� i ic � � �� �D �N �I �# iv i ii i^���i* i i@ i i� �a �x g �����������r c * C s� | dk�r�t �ttd d d t|i��� }t�ttd d d t|i��� }t�ttd d d t|i��� }t�ttd d d t|i��� }t�ttd d d t|i��� }t �ttd d d t|i��� }t
�ttd d d t|i��� }t�ttd d d t|i��� } t�ttd d d t|i��� }
t
�ttd d d t|i��� }t�ttd d d t|i��� }t�ttd d d t|i��� }
t�ttd d d t|i��� }t�ttd d d t|i��� }t�ttd d d t|i��� }t�ttd d d t|i��� }t�ttd d d t|i��� }t�ttd d d t|i��� }t�ttd d d t|i��� }t�ttd d d t|i��� }�nt td �ttd d d ttjtd d d i�td }t�|�t|i��� � }ttd �ttd d d ttjtd d d i�td }t�|�t|i��� � }ttd �ttd d d ttjtd d d i�td }t�|�t|i��� � }ttd �ttd d d ttjtd d d i�td }t�|�t|i��� � }ttd �ttd d d ttjtd d d i�td }t�|�t|i��� � }t td �ttd d d ttjtd d d i�td }t�|�t|i��� � }t
td �ttd d d ttjtd d d i�td }t�|�t|i��� � }ttd �ttd d d ttjtd d d i�td }t�|�t|i��� � } ttd �ttd d d ttjtd d d i�td }t�|�t|i��� � }
t
td �ttd d d ttjtd d d i�td }t�|�t|i��� � }ttd �ttd d d ttjtd d d i�td } t�| �t|i��� � }ttd �ttd d d ttjtd d d i�td }!t�|!�t|i��� � }
ttd �ttd d d ttjtd d d i�td }"t�|"�t|i��� � }ttd �ttd d d ttjtd d d i�td }#t�|#�t|i��� � }ttd �ttd d d ttjtd d d i�td }$t�|$�t|i��� � }ttd �ttd d d ttjtd d d i�td }%t�|%�t|i��� � }ttd �ttd d d ttjtd d d i�td }&t�|&�t|i��� � }ttd �ttd d d ttjtd d d i�td }'t�|'�t|i��� � }ttd �ttd d d ttjtd d d i�td }(t�|(�t|i��� � }ttd �ttd d d ttjtd d d i�td })t�|)�t|i��� � }|||||||| |
|||
||||||||fS )z(returns the shape-dependent coefficients� �?r r r )�F1p_def�subs�xibr �evalf�F2p_def�F3p_def�F4p_def�F5p_def�F6p_def�G1p_def�G2p_def�G3p_def�G4p_def�F1f_def�F2f_def�F3f_def�F4f_def�F5f_def�F6f_def�G1f_def�G2f_def�G3f_def�G4f_defr �I�re)*�rZe0ZF1p_effZF2p_effZF3p_effZF4p_effZF5p_effZF6p_effZG1p_effZG2p_effZG3p_effZG4p_effZF1f_effZF2f_effZF3f_effZF4f_effZF5f_effZF6f_effZG1f_effZG2f_effZG3f_effZG4f_effZF1p_tmpZF2p_tmpZF3p_tmpZF4p_tmpZF5p_tmpZF6p_tmpZG1p_tmpZG2p_tmpZG3p_tmpZG4p_tmpZF1f_tmpZF2f_tmpZF3f_tmpZF4f_tmpZF5f_tmpZF6f_tmpZG1f_tmpZG2f_tmpZG3f_tmpZG4f_tmpr r r
�shape_coeffsr s�
"""""""""""""""""""&@@@@@@@@@@@@@@@@@@@@�rd c C s| t | |�\}}}}}}}} }
}}}
}}}}}}}}tdtd d tt t| t| t| t| t| t | t
| t|
t| �
ttd d d t|t| i��� }tdtd d tt t| t|
t| t| t| t | t
| t| t| �
ttd d d t|t| i��� }tdtd d tt t| t| t| t| t| t | t
| t|
t| �
ttd d d t|t| i��� }tdtd d tt t| t|
t| t| t| t | t
| t| t| �
ttd d d t|t| i��� }| dk�r\||fS | dk�rx| dk �rx||fS d S )Nr r r rI � )rd r r rL �I1�I2�I3�I4�I5I6�J1�J2�J3�J4rK �krM )rc �eeZF1pZF2pZF3pZF4pZF5pZF6pZG1pZG2pZG3pZG4pZF1fZF2fZF3fZF4fZF5fZF6fZG1fZG2fZG3fZG4fZparticle_inertia_prolateZfluid_inertia_prolateZparticle_inertia_oblateZfluid_inertia_oblater r r
�inertial_contributions� s2 2@��@��@��@��
rq c C sL | dkr| | d d d S | dk r@| dkr@dd| d d S t d��dS )z1calculate particle eccentricity from aspect ratiorI r r r re z1Please pass a valid aspect ratio > 0.0 and != 1.0N)�
ValueError)rc r r r
�calculate_eccentricity� s
rs ��Q����?c
C s� t | �}t| |�\}}|du rXt�t�ddd�t�ddd�f�}t�|t�ddd�f�}g }g }tt|��D ]@}|| }|�t|i�} |� || g� |�t|i�} |� | � qlt�
|�}t�
|�}t�||f�S )zjreturns particle and fluid inertia orbit variations for the given aspect ratio and range of orbit costantsNg�h㈵��>g�������?�d r r )rs rq �np�concatenate�linspace�range�lenrK r �append�array�column_stack)
rc ZCrangerp ZPINEZFINEZCDC_pineZCDC_fine�jZCVAL�datar r r
�deltaC_dabade16� s "
r� )rt N).�__doc__Zsympyr �numpyrv �symbolsro r rL r r rJ rN rO rP rQ rR rS rT rU rV rW rX rY rZ r[ r\ r] r^ r_ r` �pirf rg rh ri �sqrtrj rk rl rm rn rd rq rs r� r r r r
�<module> s
T@B
R>RR�J��
��<
�
����$
�
�
�
�
��
��F&����<*�B�F�>&���FB�(
�
���
��"
�
�
����
�
�
�
�
��
��X����
F:�(
�
���
��"
�
�
����V
��>&����H:�>��
��N��.
�
�
��
��>&����FB�Z�N��H
��
��F&����
6"L,�$�@�D��8�`j8���H