a
    {d"                     @   s   d dl mZ d dlmZ d dlmZmZ d dlmZ d dl	m
Z
 d dlmZmZmZmZmZmZmZ d dlmZmZ d dlmZ d d	lmZ d d
lmZ d dlmZ ejZdd Z dd Z!dd Z"dd Z#dd Z$dd Z%dd Z&dS )    )expand)symbols)cossin)Matrix)trigsimp)PinJointJointsMethodBodyKanesMethodPrismaticJointLagrangesMethodinertia)dynamicsymbolsReferenceFrame)raises)zeros)lambdify)solvec            	      C   sJ  t d} t d}td| |}td\}}td\}}| || j  t| |}|j| jks^J |j|| gkspJ |j	| j
|| jj fgksJ |jt|gksJ |jt|gksJ |jt||  gksJ | }|t| |  ggksJ |jt|gdggksJ |jtddgd|ggks4J t|jtsFJ d S )NPCP1zC_ixx gz
q_P1, u_P1r      )r
   r   r   r   apply_forceyr	   framebodiesloads
masscenterqr   ukdesdiff	form_eomsforcing_fullmass_matrix_full
isinstancemethodr   )	r   r   ZPinZC_ixxgr   r    r'   Zsoln r)   x/var/www/html/stable-diffusion-webui/venv/lib/python3.9/site-packages/sympy/physics/mechanics/tests/test_jointsmethod.pytest_jointsmethod   s$    
 r+   c                     s   t d t d} t d}td\}}td | |td| ||tt fdd td | |d	td| ||d	tt fd
d td | ||td| |||tt fdd d S )Nr   r   Tzq ur   P2c                      s   t  S Nr	   r)   r   r   r-   r)   r*   <lambda>-       z?test_jointmethod_duplicate_coordinates_speeds.<locals>.<lambda>)speedsc                      s   t  S r.   r/   r)   r0   r)   r*   r1   1   r2   c                      s   t  S r.   r/   r)   r0   r)   r*   r1   5   r2   )r
   r   r   r   r   
ValueError)r   r,   r   r    r)   r0   r*   -test_jointmethod_duplicate_coordinates_speeds&   s    r5   c               
   C   s  t d\} }t d\}}td\}}}td}td|d}td|d}	td|||| | |j |jd	}
td
||	||| |	j |jd	}||| |j  |	|| |j  t||
|}|  t	|j
tg dg dddd|d  | t| d|d  |  |d | t| |d |  gdd|d | t| |d |  |d | ggks^J t|jtt|g|g| | | t| | t|   || | t|   |d | d| |  | t|  g| | | t| |  |d | |d  t|  ggksJ d S )Nzq1 q2zu1 u2zm l gr   r   massRJ1r3   coordinateschild_point
joint_axisJ2)r   r   r   r   )r   r   r   r   r         )r   r   r
   r   xzr   r	   r#   r   r%   r   r   r   r$   r   )q1q2u1u2mlr(   r   ZPartPZPartRr9   r>   r'   r)   r)   r*   $test_complete_simple_double_pendulum7   s8    J.4"6rI   c                  C   sr  t d\} }}}td\}}}}}td}	td|d}
td|d}td|	|
| |d}td	|
|||d}|	j||  |	j |
d
 |	j|| |	j |
d
 |
j|| |	j |d
 |
j|| |	j |d
 t|	||}|  |j}|j	}|
|}t|d t| |  ||  ||  ||  | ks,J t|d t||  ||  d| |  d| |  | ksnJ d S )Nzq1 q2 u1 u2zm c1 c2 k1 k2WB1r6   B2r9   )r;   r3   r>   )Zreaction_bodyr   r   r?   )r   r   r
   r   r   rA   r	   r#   mass_matrixforcingLUsolver   )rC   rD   rE   rF   rG   Zc1c2Zk1Zk2rJ   rK   rL   r9   r>   r'   MMrN   rhsr)   r)   r*   test_two_dof_jointsQ   s0    
<(rS   c            	   	   C   s   t d\} }}td}td|d}td}td|||t||  |j |jd}| | |  t| |_	t
||}|t | }|d | t| |  ksJ d S )	Nzl m gr   br6   r   r   r:   r   )r   r
   r   r   r"   trA   rB   r   Zpotential_energyr	   r#   r   rR   r   )	rH   rG   r(   r   rT   r   r   r'   rR   r)   r)   r*   test_simple_pedulumf   s    

rV   c               	   C   s
  t d\	} }}}}}}}}td\}	}
}}td}td}td| |t|||dd}td||t||||d}td	}td
|||	|| |j |jd}td|||
||| |j |jd}|| | |j  ||| |j  t	|||}|
  |j}|j}||}d| | | t|
 t|
 d| | | t|
 t|
  || |  t|	  || | t|	  ||t|
d   |t|
d   |d |   |d |   }|d |  dksJ || |d  t|
 t|
 | }|d |  dksJ d S )Nz)mA, mB, lA, lB, IAxx, IBxx, IByy, IBzz, gztheta phi omega alphaABrodr   )r7   r   central_inertiaplater   r9   )r;   r3   r<   r=   r>   )r;   r3   parent_pointr=   r?   r   )r   r   r   r
   r   r   rB   r   r   r	   r#   rM   rN   rO   r   r   Zsimplify)ZmAZmBZlAZlBZIAxxZIBxxZIByyZIBzzr(   thetaphiomegaalpharW   rX   rY   r[   r   r9   r>   r'   rQ   rN   rR   Zxdr)   r)   r*   test_chaos_pendulums   sP    
4


$rb   c            &         s8  t d\} }}}}}td\}}}}	td  fdd||||	fD }
td | |
d d}td	| |
d
 d}td| |
d d}td|	 |
d d}td||| ||j|d |j | d |j d}td|||||j|d |j | d |j d}td|||||j|d |j |	 d |j d}|j|j|d |j  |	d |j  }t	|
|j|
|jg}t||||}t j}t|j| |||||g}|||}t|j| g|g||g||g|j|||j|jd
}| \}}|td
ksJ t	||||	g}t	| ||g}t	|||g}t||f|j}t|||f|j}t|||f|} g d}!g d}"g d}#t	g dg dg dg}$t	dgdgdgg}%dtfdd | |"|#|!D sJ tfd!d t	||"|!|$ D sJ tfd"d t	||"|#|!|% D s4J d S )#Nz
q1:4, u1:4z	l1:5, rhoNc              	      s&   g | ]}t  d d |d  d qS )r   r@      )r   ).0rH   )rc   rhor)   r*   
<listcomp>   r2   zAtest_four_bar_linkage_with_manual_constraints.<locals>.<listcomp>ZLink1r   )r   r7   rZ   ZLink2r   )r7   rZ   ZLink3r?   ZLink4r@   r9   )r;   r3   r=   r\   r<   r>   ZJ3)	Zq_indZu_indZq_dependentZu_dependentZkd_eqsZconfiguration_constraintsZvelocity_constraintsZ	forcelistr   )gp=
ף?gQ?gzG?g(\?i  )g @gtM)L?gF!8@)g?g68[ƿgൄ?)gDwCA@g_'@gY>)g    gTB?gv1?)g_r=
ףg0 Sg;?gLgd`Egop]?g|=c                 3   s   | ]}t | k V  qd S r.   absre   rA   epsr)   r*   	<genexpr>   r2   z@test_four_bar_linkage_with_manual_constraints.<locals>.<genexpr>c                 3   s   | ]}t | k V  qd S r.   rh   rj   rk   r)   r*   rm      r2   c                 3   s   | ]}t | k V  qd S r.   rh   rj   rk   r)   r*   rm      r2   )r   r   r   r
   r   rB   rA   r   Zpos_fromr   dotr   r	   _tr   r!   r"   subsr   r   r   r   Zkanes_equationsr   r   rM   rN   all)&rC   rD   Zq3rE   rF   u3l1l2l3l4ZinertiasZlink1Zlink2Zlink3Zlink4Zjoint1Zjoint2Zjoint3Zloopfhr'   rU   ZqdotsZfhdZkanefrZfrspr   r    Zeval_mZeval_fZeval_fhdZp_valsZq_valsZu_valsZ
mass_checkZforcing_checkr)   )rc   rl   rf   r*   -test_four_bar_linkage_with_manual_constraints   s~    $$rz   N)'Zsympy.core.functionr   Zsympy.core.symbolr   Z(sympy.functions.elementary.trigonometricr   r   Zsympy.matrices.denser   Zsympy.simplify.trigsimpr   Zsympy.physics.mechanicsr   r	   r
   r   r   r   r   Zsympy.physics.vectorr   r   Zsympy.testing.pytestr   Zsympy.core.backendr   Zsympy.utilities.lambdifyr   Zsympy.solvers.solversr   ro   rU   r+   r5   rI   rS   rV   rb   rz   r)   r)   r)   r*   <module>   s$   $ 