
    sh                        S SK Js  Jr  S SKrS SKrS SKr	\R                  " SSS9u  rrrr\R                  " S5      u  rrrr\R                  " SS5      u  rrrr\R                  " SS	5      u  rr\R4                  " S
5      r\R8                  " S5      r\R=                  \S 5        \R4                  " S5      r\R@                  " S\\\R                  " S5      \RB                  " \RD                  \RD                  5      \45      r#\R8                  " S5      r$\$R=                  \S 5        \R4                  " S5      r%\R@                  " S\$\%\R                  " S5      \RB                  " \%RD                  \%RD                  5      \$45      r&\RO                  \S\\RP                  /5        \%RO                  \S\\RR                  /5        \R8                  " S5      r*\\S	-  -
  S	-  r+\RY                  \*\+\RR                  -  5        \$RY                  \*\\RR                  -  5        \R[                  \\\RP                  -  5        \%R[                  \\\RR                  -  5        \*R=                  \S 5        \R]                  \*\\5        \$R]                  \*\\5        \R                  " S5      r/\/\#l0        \R                  " S5      r1\1\&l0        S\/-  S	\+-  S	-  -  r2\2r3S r4S\1-  \S	-  -  r5S\1-  \S	-  \S	-  -   -  r6S\1-  \S	-  -  r7\Rp                  " \\2\3\4S S S 5      \4\#l8        \Rp                  " \%\5\6\7S S S 5      \$4\&l8        \#R`                  \\RR                  -  -  r9\&R`                  \\RR                  -  -  r:\\-
  \\-
  /r;\#Rx                  \#R`                  \\RR                  -  -  4\&Rx                  \&R`                  \\RR                  -  -  4/r=\R|                  " \\\/\\/\;S9r?\?R                  \#\&/\=5      u  rArB\A\B-   rCS SKDJErE  \E" \?\S\S\S\S\/S\1S00 \\	R                  " S5      \\	R                  " S5      \S \S 0\	R                  " SS S!5      S"9rH\HR                  5       r(g)#    Nzg lb w hT)realztheta phi omega alphaztheta_ phi_ omega_ alpha_   ztheta_ phi_   na_cma_famb_cmb_fbAxisomambgUUUUUU?)q_indu_indkd_eqs)SystemgQ#@g?g?g{Gz?Z   g      ?g        
   g     @@)	constants
specifiedsinitial_conditionstimes)Jsympy.physics.mechanicsphysics	mechanics_mesympy_smmathr
   numpy_npsymbolsglbwhdynamicsymbolsthetaphiomegaalphatheta_dphi_domega_dalpha_dtheta_ddphi_ddReferenceFrameframe_nPoint	body_a_cmset_velbody_a_f	RigidBodyouterxbody_a	body_b_cmbody_b_fbody_borientyzpoint_olaset_posset_ang_velv2pt_theoryr   massr   iaxxiayyiazzibxxibyyibzzinertiaforce_aforce_br   
masscenter	forceListKanesMethodkanekanes_equationsfrfrstarzeropydy.systemr   deg2radlinspacesys	integrate     ژ/Users/tiagomarins/Projetos/claudeai/copy_bank/venv/lib/python3.13/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/chaos_pendulum.py<module>rd      s=   % %   kk*402q!--.EF sE5#&#5#56QST#U  %%mQ7 &


S
!IIf	 	  '1 e$	sIxS1ACIIhjjYaYcYcDdenCo	pIIf	 	  '1 e$	sIxS1ACIIhjjYaYcYcDdenCo	p %!3 4 &3

"3 4
))C.1faZ 	  '2hjj= ) 	  '2hjj= )   WeGIIo .   XuXZZ/ 0   	  ggh / 	  ggh /[[[[Bw"qyBwq!t|Bw1QT	Bwq!t|++hdD!QBIN++hdD!QBIN
++q{
#
++q{
#
E/55=	)Qwyy[ 9:V=N=Nv{{\]^e^g^g\gOh<ij	
wuSk%RXY!!66"2I>
F	&y T$3#qbr#N#++b/3s{{3/?q%PQRS"g&(
 --/rb   