U
    0e2.                     @   s   d dl mZmZmZmZmZmZmZmZ d dl	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mZmZmZmZ d dlmZ edd Zd	d
 Zdd Zdd Z dd Z!dd Z"dS )    )symbolsMatrixcossinatansqrtRational_simplify_matrix)sympify)simplify)solve)dynamicsymbolsReferenceFramePointdotcrossinertiaKanesMethodParticle	RigidBody
LagrangianLagrangesMethod)slowc            ;         s  t d\} }}}td \}}}}}}	}
fdd|
D  \}}}}}}}td}td \}}}}}}}fdd|D \}}}}}}tdtd	}d
d|jg} | dd|| jg}!|!dd||!jg |d|j |j  |	j   	|!	}" 
||!j ||!j  ||!j   || j | j  | j   d| |!j   t|	tj g}#tfdd D }$t fdd|!D fddD  }%t|%|}&|!
|"|&   	|!t|!	 	  || | j }'|| d  d }(|| d  d })t |(|)|(}*td ||*f}+|+g},|'fg}-t|||||g|||g|%|	g|#|||g|$d}.|.|,|-\}/}0|. }1|1j|#kst|1j|$kst|1j|$|. ks"tt|1j |1j! |}2|&" D ]}3|2|3 |&|3 ks<tq<t#|1j$|1j% |/ |0 tdddgkst|	|  t&| i}4|d|t'|| | |t&|| ||  t'|| |  t&| |d||  t'|| |  t'| i}5|d||  t'|| |  t&| ||  t'|| |  t'| |di}6|d| t'| d|   t'd| |d  d  dt&| | | d  |d|d|| t'|t'| | | t'||d    || d| t'| d|   t'd| |d  d  dt&| | | d   ||  t'|t&| | | t&||d    i}7|1j(|4|5|6|7gddd\} }!|d|d|d| d|di}8tddddddddgddddddddgddddddddgt'|| ddddt'| t&| dgt&| | ddddt&|t'| dgdt)dddddddd| d gddddddddgdddddd| ddgg}9tg }:| |8|9ks`t|!|8|:ksttt*| |8|dt+d , ddikstd S ) Nz	t r m g vzq1:7c                    s   g | ]}|  qS  diff).0qitr   P/tmp/pip-unpacked-wheel-_6tpq7m6/sympy/physics/mechanics/tests/test_linearize.py
<listcomp>   s     z4test_linearize_rolling_disc_kane.<locals>.<listcomp>zu:6zu1:7c                    s   g | ]}|  qS r   r   )r   uir   r   r    r!      s     NNOAAxisBCCOPc                    s   g | ]}t  |qS r   r   velr   Zuv)r#   r*   r   r    r!   7   s     c                    s    g | ]}t   |qS r   )r   
ang_vel_inr-   )r(   r#   w_c_n_qdr   r    r!   :   s     c                    s    g | ]}t   |qS r   r+   r-   )r)   r#   	v_co_n_qdr   r    r!   ;   s           Disc)kd_eqsq_dependentconfiguration_constraintsu_dependentvelocity_constraintsr         Top_pointA_and_Br            )-r   r   r   r   	orientnewzxy	locatenewr.   set_ang_velpos_fromdtset_velv2pt_theoryr   r   r   subsZset_ang_accr   r   r   r   kanes_equationsZto_linearizerf_cAssertionErrorf_vf_ar   ZkindiffdictZf_0Zf_1keysr   Zf_2Zf_3r   r   	linearizer   r
   r   Z	eigenvals);rmgvq1q2q3Zq4Zq5Zq6qq1dq2dq3dZq4dZq5dZq6dqduu1u2u3Zu4Zu5Zu6u1du2dZu3dZu4dZu5dZu6dr$   r%   r'   Zw_b_n_qdrN   rP   ZkindiffsZqdotsZF_COIJZI_C_COr3   ZBLZFLKMfrZfr_starZ
linearizersolr   q_opu_opZqd_opud_opZupright_nominalZA_solZB_solr   )r(   r)   r#   r*   r   r0   r/   r     test_linearize_rolling_disc_kane   s    "&

&&
.
   ,  
      H   * J ,&& rn   c                  C   s6  t d} t d}t dd}td\}}}d}td}td}||d |d	d
| |jg}	|	|||j  |d||	j	 }
|

|||	 td|
|}t|| g}|| |j	 }t|| g|g|d}||g|
|fg\}}|jddd\}	}}|	tddgdt|  | dggks t|tg ks2td S )NrX   ra   r>   L, m, t皙#@r#   N*r   r%   axisr*   pP)q_indu_indr4   T)r=   r   皙#)r   r   r   r   rJ   rB   rC   rG   rF   rD   rK   r   r   r   rM   rS   r   rO   )rX   ra   r\   LrU   r   rV   r#   pNr%   r*   rs   kdeRrh   ri   frstarr'   inp_vecr   r   r    $test_linearize_pendulum_kane_minimal   s(    
*r}   c                   C   s  t d\} }t ddd\}}t d\}}t ddd\}}td\}}	}
d}td}td}||d	 t||  }|d
d||jg}|d| |j	 ||j
  }td||	}t|| || g}t|||g}|||||| t|| | g}t||||j	g}|  ||
}|  |	| |j	 }t||g|g| g|g||||d	}||g||fg\}}| ||d	i}|d	|d	i}|d	|d	i}|j|||gddd\}}}| td	dgd| d	ggkst|tg kstd S )Nq1:3r>   levelzu1:3ro   rp   r#   rq   r   r%   rr   P1rs   )rt   ru   r5   r7   r6   r8   Zacceleration_constraintsr4   Tr;   rv   )r   r   r   r   rJ   r   rB   rC   rF   rD   rE   r   r   r   rH   rI   rL   Z	magnituder,   Zexpressr   r   r   r   rM   rS   expandrO   ) rX   rY   r\   r]   ra   rb   rd   re   rw   rU   r   rV   r#   rx   theta1r%   r*   rs   ry   Zdq_dictrN   rP   rQ   rz   rh   ri   r{   rk   rl   rm   r'   r|   r   r   r    'test_linearize_pendulum_kane_nonminimal   sP    
   &r   c                  C   s$  t d} t dd}td\}}}d}td}td}||d |dd	| |jg}||||j  |d
||j	 }	|	
||| td|	|}
t||
}t|| g|	|| |j	 fg|d}|  |j| g|gdd\}}}t|tddgdt|  | dggkst|tg ks td S )NrX   r>   ro   rp   r#   rq   r   r%   rr   r*   rs   )	forcelistframeT)r=   rv   )r   r   r   r   rJ   rB   rC   rG   rF   rD   rK   r   r   r   form_lagranges_equationsrS   r	   r   r   rO   )rX   r\   rw   rU   r   rV   r#   rx   r%   r*   rs   LagLMr'   r|   r   r   r    (test_linearize_pendulum_lagrange_minimal   s$    

".r   c                  C   s  t d\} }t ddd\}}td\}}}d}td}td}	|	|d t||  }
|d	d
|
|jg}|	d| |j	 ||j
  }||||	| td||}t| d |d  |d  g}t||}t|| |g|||| |j	 fg|d}|  | ||d|d|d||d||di}|j|d}|| |j|g|g| g|g|dd\}}}t|tddgd| dggkst|tg kstd S )Nr~   r>   r   ro   rp   r#   rq   r   r%   rr   r   rs   r1   )Z
hol_coneqsr   r   )r<   T)r<   r=   rv   )r   r   r   r   rJ   r   rB   rC   rF   rD   rE   rH   rI   r   r   r   r   r   r   Zsolve_multipliersupdaterS   r	   rO   )rX   rY   r\   r]   rw   rU   r   rV   r#   rx   r   r%   r*   rs   rN   r   r   r<   Zlam_opr'   r|   r   r   r    +test_linearize_pendulum_lagrange_nonminimal
  s2    
&(
 &r   c                  C   s  t d \} }}}t dd \}}}}td\}}	}
td}|dd| |jg}|dd||jg}|dd||jg}td	}||d
 |	d||j }|
||| t||	d |d  |	d |d  |	d |d  }td|||	||f}|	 |
 | t| |_t||}t||}|  | d
|d
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| d
| d
| d
i}|j|||ddd
 }td
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d| d
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 d|  d
d| d d
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gg}||kstd S )Nzq1 q2 q3r>   zr m gr#   Yr&   rw   rz   r(   r   Dmcr2   r1   BodyDT)rt   Zqd_indr<   r=   ir9   r:   )r   r   r   rB   rC   rD   rE   r   rJ   rF   rK   r   r   r   Zpotential_energyr   r   r   r   rS   r   rO   )rX   rY   rZ   r[   r\   r]   r^   r_   rT   rU   rV   r#   r   rw   rz   r(   r   rf   r   r   lr<   r%   rj   r   r   r    $test_linearize_rolling_disc_lagrange+  sL    2

        "r   N)#Zsympy.core.backendr   r   r   r   r   r   r   r	   Zsympy.core.sympifyr
   Zsympy.simplify.simplifyr   Zsympy.solvers.solversr   Zsympy.physics.mechanicsr   r   r   r   r   r   r   r   r   r   r   Zsympy.testing.pytestr   rn   r}   r   r   r   r   r   r   r   r    <module>   s   (4
y%@!