
    Qi                     4   d dl mc mZ d dlZd dlZd dlZ	 ej
        dd          \  ZZZZ ej        d          \  ZZZZ ej        dd          \  ZZZZ ej        dd	          \  ZZ ej        d
          Z 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          Z# 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          Z&e'                    edeej(        g           e%'                    edeej)        g            ej        d          Z*eed	z  z
  d	z  Z+e,                    e*e+ej)        z             e$,                    e*eej)        z             e-                    eeej(        z             e%-                    eeej)        z             e*                    ed            e.                    e*ee           e$.                    e*ee            ej
        d          Z/e/e#_0         ej
        d          Z1e1e&_0        de/z  d	e+z  d	z  z  Z2e2Z3d Z4de1z  ed	z  z  Z5de1z  ed	z  ed	z  z   z  Z6de1z  ed	z  z  Z7 ej8        ee2e3e4d d d           efe#_8         ej8        e%e5e6e7d d d           e$fe&_8        e#j0        eej)        z  z  Z9e&j0        eej)        z  z  Z:eez
  eez
  gZ;e#j<        e#j0        eej)        z  z  fe&j<        e&j0        eej)        z  z  fgZ= ej>        eeegeege;          Z?e?@                    e#e&ge=          \  ZAZBeAeBz   ZCd dlDmEZE  eEe?edededede/de1dii e e	jF        d          e e	jF        d          ed ed i e	jG        dd d!          "          ZHeHI                                Z(dS )#    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     /var/www/development/aibuddy-work/election-extract/venv/lib/python3.11/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/chaos_pendulum.py<module>rd      s   % % % % % % % % %            ck*40002q!-3-.EFF sE5#53#56QST#U#U  %3%mQ77 &
#
S
!
!CIf	 	  '1   3e$$	sIxS1A1AICIhjYaYcDdDdenCo	p	pCIf	 	  '1   3e$$	sIxS1A1AICIhjYaYcDdDdenCo	p	p %!3 4 4 4 &3
"3 4 4 4
#)C..1faZ 	  '2hj= ) ) ) 	  '2hj= ) ) )   WeGIo . . .   XuXZ/ 0 0 0     	  ggh / / / 	  ggh / / /S[S[Bw"qyBwq!t|Bw1QT	Bwq!t|#+hdD!QBBIN#+hdD!QBBIN
+q{
#
+q{
#
E/55=	)Qwy[ 9:V=Nv{\]^e^g\gOh<ij	swuSk%RXYYY!!66"2I>>
F	&y      fT$3#qbr#N+#+b//3{s{3/?/?q%PQRS"g&&( ( (
 --//rb   