Book a Demo!
CoCalc Logo Icon
StoreFeaturesDocsShareSupportNewsAboutPoliciesSign UpSign In
Download
602 views
unlisted
ubuntu2404
a

�6i�4�@sdZddlZddlZe�d�Zejddd�Zejddd�Ze�d�Z	d	d
�Z
dedded
ded
e
e�e
e�ededd
ed
d
Zede
e�eee
e�ddedd
ed
d
Zed
ed
e
e�e
e�ededd
ed
d
Z
e
Ze
d
ZeZdedded
d
ed
de
e�ededd
ed
d
Zeedeedde
e�ddd
ed
d
Zeed
Zeed
Zed
deddeddeddeddedded
dded
deddedd edd!ed
dede
e�dd"ed#edd$edd%edd&edd'edd(ed
d)ede
e�ded*edd+edd,edd-edd.edd/edd0ed
d1e
e�dd2ed!d3edd4edd5edd6edd7edd8edd9ed
d:e
e�d
d;ed
d<d
ed
dd=ed
ded
ee
e�d
d=eddedede
e�ded
de
e�ded<Zed
d>ed"d?edd@eddAedded"eded
ded
e
e�ddedd"eddeddBed
dee
e�d
deddCeddDeddEeddFed
de
e�ded
edd
d=ed
ded
ee
e�d
d=eddedede
e�d<Zed
dGeddHeddIeddJeddKed
dLded
dededded
dede
e�dd"ededdMeddNeddOeddPed
dede
e�ddQedRdSedTdUed"dVeddWeddXeddYee
e�ddZeddGedd[edd\edd]edd^edd_ed
d`e
e�d
d;ed
d<d
ed
dd=ed
ded
ee
e�d
d=eddedede
e�ded
de
e�ded<ZeZedaZedaZed
dbeddcedddeddeeddfed
dgd"ed
d"edded
d
ede
e�ddedheddieddjeddkeddled
dmede
e�ddnedRdoedTdped"dqeddreddseddtee
e�dueddveddweddxeddyeddzedd{ed
d|e
e�d
ded
edd
d=ed
ded
ee
e�d
d=eddedede
e�ded
de
e�ded<Zed
dedd}edd~eddeddDed
d|d"eddedd
ed
dede
e�ddedtedd�edd�eddjedd�ed
dede
e�dedhedd�edd�edd�edd@edd)ed
de
e�d�edd�edd�edd�edd�edd�edd�ed
de
e�d
ded
edd
d=ed
ded
ee
e�d
d=eddedede
e�ded
de
e�ded<Zed
dGeddHeddIeddJeddKed
dLded
dededded
dede
e�dd"ededdMeddNeddOeddPed
dede
e�ddQedRdSedTdUed"dVeddWeddXeddYee
e�ddZeddGedd[edd\edd]edd^edd_ed
d`e
e�d
d�ed
d
ed
ddd=ed
ded
ee
e�d
d=eddedede
e�ded
de
e�ded<ZeZd
ejZ d
ejededd<Z!d
ejd
e	d
de	d
ed
dd�dZ"d
ejedd
edd�Z#dejd
ed
de�$e	d
de	d
ed
d�de	d
ddee�$e	d
de	d
ed
d�e�$e	d
de	d
ed
d�dde	d
dede�$e	d
de	d
ed
d�ede�$e	d
de	d
ed
d�d!e	de	d
d
d
ed
dd
e�$e	d
de	d
ed
d�d<Z%ejed
dedd�Z&ejd�e	d
de	d
ed
dd�e	d
edd
de	d�ed
dd<Z'ejedd
edd�Z(ejed
dde	dede	d
eddded
e�$e	d
de	d
ed
d�ded
de�$e	d
de	d
ed
d�de	d�ed
dd=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}�CcCsdt�|d|d�S)N��?�)�sym�log)�val�r	�\/Users/davide/Downloads/Joint_paper_figures/jupyter_notebook_submission/figure_5/Dabade16.py�invcothsr�����r�(�ix����iF�
i��iA.�i5$i�������	i i4�ii�i�i 
ilil6i�Ri�7iAi�
i�ii�i�i�i�i�i�
iQ�:i�����������i������s�Z��W��!�4izi!i{i�iA	iV���i�i4����
iD�i�i�(iiO�,���mi�i�ii7�g@�Qi�i2i�i��6�l���E���i����ii�i=i��O�$i�i�i�i
��iic�����D�N�I�#iviiii^���i*ii@ii��a�xg�����������rc*Cs�	|dk�r�t�ttdddt|i���}t�ttdddt|i���}t�ttdddt|i���}t�ttdddt|i���}t�ttdddt|i���}t	�ttdddt|i���}t
�ttdddt|i���}t�ttdddt|i���}	t�ttdddt|i���}
t
�ttdddt|i���}t�ttdddt|i���}t�ttdddt|i���}
t�ttdddt|i���}t�ttdddt|i���}t�ttdddt|i���}t�ttdddt|i���}t�ttdddt|i���}t�ttdddt|i���}t�ttdddt|i���}t�ttdddt|i���}�nttd�ttdddttjtdddi�td}t�|�t|i����}ttd�ttdddttjtdddi�td}t�|�t|i����}ttd�ttdddttjtdddi�td}t�|�t|i����}ttd�ttdddttjtdddi�td}t�|�t|i����}ttd�ttdddttjtdddi�td}t�|�t|i����}t	td�ttdddttjtdddi�td}t�|�t|i����}t
td�ttdddttjtdddi�td}t�|�t|i����}ttd�ttdddttjtdddi�td}t�|�t|i����}	ttd�ttdddttjtdddi�td}t�|�t|i����}
t
td�ttdddttjtdddi�td}t�|�t|i����}ttd�ttdddttjtdddi�td} t�| �t|i����}ttd�ttdddttjtdddi�td}!t�|!�t|i����}
ttd�ttdddttjtdddi�td}"t�|"�t|i����}ttd�ttdddttjtdddi�td}#t�|#�t|i����}ttd�ttdddttjtdddi�td}$t�|$�t|i����}ttd�ttdddttjtdddi�td}%t�|%�t|i����}ttd�ttdddttjtdddi�td}&t�|&�t|i����}ttd�ttdddttjtdddi�td}'t�|'�t|i����}ttd�ttdddttjtdddi�td}(t�|(�t|i����}ttd�ttdddttjtdddi�td})t�|)�t|i����}||||||||	|
|||
||||||||fS)z(returns the shape-dependent coefficients��?rrr)�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_coeffsrs�
"""""""""""""""""""&@@@@@@@@@@@@@@@@@@@@�rdcCs|t||�\}}}}}}}}	}
}}}
}}}}}}}}tdtddttt|t|t|t|t|t	|t
|	t|
t|�
ttdddt|t|i���}tdtddttt|t|
t|t|t|t	|t
|t|t|�
ttdddt|t|i���}tdtddttt|t|t|t|t|t	|t
|	t|
t|�
ttdddt|t|i���}tdtddttt|t|
t|t|t|t	|t
|t|t|�
ttdddt|t|i���}|dk�r\||fS|dk�rx|dk�rx||fSdS)NrrrrI�)rdrrrL�I1�I2�I3�I4�I5I6�J1�J2�J3�J4rK�krM)rc�eeZF1pZF2pZF3pZF4pZF5pZF6pZG1pZG2pZG3pZG4pZF1fZF2fZF3fZF4fZF5fZF6fZG1fZG2fZG3fZG4fZparticle_inertia_prolateZfluid_inertia_prolateZparticle_inertia_oblateZfluid_inertia_oblater	r	r
�inertial_contributions�s22@��@��@��@��
rqcCsL|dkr||dddS|dkr@|dkr@dd|ddStd��dS)z1calculate particle eccentricity from aspect ratiorIrrrrez1Please pass a valid aspect ratio > 0.0 and != 1.0N)�
ValueError)rcr	r	r
�calculate_eccentricity�s
rs��Q����?c
Cs�t|�}t||�\}}|durXt�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�������?�drr)rsrq�np�concatenate�linspace�range�lenrKr�append�array�column_stack)
rcZCrangerpZPINEZFINEZCDC_pineZCDC_fine�jZCVAL�datar	r	r
�deltaC_dabade16�s "

r�)rtN).�__doc__Zsympyr�numpyrv�symbolsrorrLrrrJrNrOrPrQrRrSrTrUrVrWrXrYrZr[r\r]r^r_r`�pirfrgrhri�sqrtrjrkrlrmrnrdrqrsr�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