
    sg                        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j4                  d
      Z ej8                  d      Zej=                  ed         ej4                  d      Z ej@                  dee ej                  d       ejB                  ejD                  ejD                        ef      Z# ej8                  d      Z$e$j=                  ed         ej4                  d      Z% ej@                  de$e% ej                  d       ejB                  e%jD                  e%jD                        e$f      Z&ejO                  edeejP                  g       e%jO                  edeejR                  g        ej8                  d      Z*eed	z  z
  d	z  Z+ejY                  e*e+ejR                  z         e$jY                  e*eejR                  z         ej[                  eeejP                  z         e%j[                  eeejR                  z         e*j=                  ed        ej]                  e*ee       e$j]                  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jp                  ee2e3e4d d d       efe#_8         ejp                  e%e5e6e7d d d       e$fe&_8        e#j`                  eejR                  z  z  Z9e&j`                  eejR                  z  z  Z:eez
  eez
  gZ;e#jx                  e#j`                  eejR                  z  z  fe&jx                  e&j`                  eejR                  z  z  fgZ= ej|                  eeegeege;      Z?e?j                  e#e&ge=      \  ZAZBeAeBz   ZCd dlDmEZE  eEe?edededede/de1dii e e	j                  d      e e	j                  d      ed ed i e	j                  dd d!      "      ZHeHj                         Z(y)#    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     w/var/www/html/venv/lib/python3.12/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/chaos_pendulum.py<module>rd      sm   % %   ckk*402q!-3--.EF sE5#53#5#56QST#U  %3%%mQ7 &
#

S
!CIIf	 	  '1 3e$	sIxS1AICIIhjjYaYcYcDdenCo	pCIIf	 	  '1 3e$	sIxS1AICIIhjjYaYcYcDdenCo	p %!3 4 &3

"3 4
#))C.1faZ 	  '2hjj= ) 	  '2hjj= )   WeGIIo .   XuXZZ/ 0   	  ggh / 	  ggh /S[[S[[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	swuSk%RXY!!66"2I>
F	&y T$3#qbr#N+#++b/3{s{{3/?q%PQRS"g&(
 --/rb   