
    g
              
       j   d dl mc mZ d dlZd dlZd dlZ	 ej
        d          \  ZZ ej        dd          \  ZZeeez  ez   dz  z  Z ej        eeg                              dd          Ze                                Z ej        d eD                                           ej        d          ej        d                   Z ej        ee          Z ej        d	 eD                                           ej        d          ej        d                   Z ej        d gg          Zeez  eez  z   ed <   e                    ej        d           ej        d gg                    Zdez  ez  d
ez  ez  z
  eej        d          dz
  <    e ej        eee                      ej        eee          e         Zeez   dz  dedz  z  z   Ze                    e            ej        dd          \  ZZZ ej        eeed g                              dd          Z ej        d eD                                           ej        d          ej        d                   Z ej        d e                                                                D                       Z  ej        d e!                                D                                           ej        d          ej        d                   Z" ej#        d          Z$ ej#        d          Z%e%&                    e$dee$j        g           e%&                    e$dej'        dz  e$j        g            ej        dd          \  Z(Z)Z*e(e%j        z  e)e%j        z  z   e*e%j+        z  z   Z, ej-        d          Z. ej-        d          Z/e.0                    e/e(e%j        z             e,1                    e$          Z,e.0                    e/e.2                    e/          1                    e$                     e%3                    e$e*e%j+        z              ee$4                    e%                     e/5                    e.e$e%            ej6        d ej-        d           ej7        d                    Z8 ej6        d ej-        d           ej7        d                    Z9e9j:        5                    e8j:        e$e%           e/;                    e8j:        e$e%            ej-        d          Z<e<=                    e$d             ej#        d          Z> ej?        de<e> ej        d           ej@        e>j        e>j                  e<f          ZA ej-        d          ZBeB=                    e$d             ej#        d          ZC ej?        deBeC ej        d           ej@        eCj        eCj                  eBf          ZD ej        d d          ZEe8jF        eEe$j        z  z  ZGe9jF        eEe$j        z  z  ZHeAjF        eEe$j        z  z  ZIeDjF        eEe$j        z  z  ZJ ej
        d!          Z+ee%j        z  ee%j+        z  z   Z,e.0                    e/ee%j        z  ee%j        z  z              e,K                    ede+z  ee+i          Z,e.0                    e/e.2                    e/          K                    ede+z  ee+i                     d"eez  e%j        z  z  ZLe8jF        eEe$j        z  z  eez  e%j        z  z   ZGdS )#    Nzx yza bT)real      c                 6    g | ]}|                                 S  )expand.0is     j/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/parsing/autolev/test-examples/ruletest10.py
<listcomp>r      s     &&&q

&&&    c                 B    g | ]}t          j        |t                    S r   )_smfactorxr	   s     r   r   r      s"    +++A
1Q+++r      za b cc           
      b    g | ],}|                     t          d t          dt          di          -S )r   r   r   )subsabcr	   s     r   r   r      s0    22211Qq1&&222r   c                 6    g | ]}|                                 S r   evalfr	   s     r   r   r      s     BBBQqwwyyBBBr   c                 N    g | ]"}|d          d                                          #S )r   r   r   r	   s     r   r   r      s(    @@@QqT!W]]__@@@r   nr   Axiszc1 c2 c3opp1p1_ptmp2p2_ptb1_cmb1_fb1b2_cmb2_fb2gz)Msympy.physics.mechanicsphysics	mechanics_mesympyr   mathr#   numpy_npdynamicsymbolsr   ysymbolsr   r   eMatrixreshaper   shaper   eqn
row_insertprintsolverhs_ycollectr   m2	eigenvalskeyseigvalue
eigenvectseigvecReferenceFrameframe_nframe_aorientpic1c2c3r-   vPointpoint_opoint_pset_posexpresspos_fromset_ang_vel
ang_vel_inv2pt_theoryParticleSymbolparticle_p1particle_p2pointa2pt_theory
body_b1_cmset_vel	body_b1_f	RigidBodyouterbody_b1
body_b2_cm	body_b2_fbody_b2r,   massforce_p1force_p2force_b1force_b2r   force_or   r   r   <module>rq      sT   % % % % % % % % %            s%  1s{5t$$$1qs1uqjLCJ!ua##HHJJCJ&&A&&&''//	!qilKKCJq!CJ+++++,,44aYq\A9Q<PPcj1#	
1QqSA	nnSYq\:3:se#4#455c!eAaCEkCIaLN  iciAa   	#a1qS1HQq!tVO 		!
#+gD
)
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)1aCJ!Aay!!!Q''SZ2222233;;QIaL1)TU,WW3:BB2..*:*:*?*?*A*ABBBCC	@@roo.?.?@@@	A	A	I	I"(ST+WYW_`aWb	c	c
#
S
!
!
#
S
!
! wGI / / / w79 5 6 6 6S[$///
BwyLGIbl*
#)C..
#)C.. GI & & &KK '**733<<WEE F F F   GR	\ * * * g!! " " "   GGG , , ,cl47!3!3ZSZ__EEcl47!3!3ZSZ__EE    k/ @ @ @   K%gg 6 6 6SYw
 
  7A   Cv&&	
#-j)[S[5E5E		R[R]^g^iHjHjkuGv
w
wSYw
 
  7A   Cv&&	
#-j)[S[5E5E		R[R]^g^iHjHjkuGv
w
wCK$Qwy[)Qwy[)<79%<79%CsgiK') 79Qwy[0 1 1 1HHa!Qq\ '**733991QqS!A,GG H H H
ac')m
Qwy[)1Q3wy=8r   