o
    GZh3                     @   s   d dl 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)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syJ |1j|$ksJ |1j|$|. ksJ t|1j|1j  |}2|&! D ]}3|2|3 |&|3 ksJ qt"|1j#|1j$ |/ |0 tg dksJ |	|  t%| i}4|d|t&|| | |t%|| ||  t&|| |  t%| |d||  t&|| |  t&| i}5|d||  t&|| |  t%| ||  t&|| |  t&| |di}6|d| t&| d|   t&d| |d  d  dt%| | | d  |d|d|| t&|t&| | | t&||d    || d| t&| d|   t&d| |d  d  dt%| | | d   ||  t&|t%| | | t%||d    i}7|1j'|4|5|6|7gddd\} }!|d|d|d| d|di}8tg dg dg d t&|| ddddt&| t%| dgt%| | ddddt%|t&| dgdt(dddddddd| d gg d!dddddd"| ddgg}9tg }:| |8|9ksJ |!|8|:ks!J t)| |8|dt*d# + dd$iks9J |.jd%d&}1|1j'|4|5|6|7gddd\} }!| |8|9ksWJ |!|8|:ksaJ d S )'Nz	t r m g vzq1:7c                       g | ]}|  qS  diff).0qitr   [/var/www/auris/lib/python3.10/site-packages/sympy/physics/mechanics/tests/test_linearize.py
<listcomp>       z4test_linearize_rolling_disc_kane.<locals>.<listcomp>zu:6zu1:7c                    r   r   r   )r   Zuir   r   r    r!      r"   NNOAAxisBCCOPc                    s   g | ]
}t  |qS r   r   velr   Zuv)r#   r*   r   r    r!   6   s    c                        g | ]}t   |qS r   )r   
ang_vel_inr-   )r(   r#   w_c_n_qdr   r    r!   9        c                    r.   r   r+   r-   )r)   r#   	v_co_n_qdr   r    r!   :   r1         Disc)kd_eqsq_dependentconfiguration_constraintsu_dependentvelocity_constraints)r   r   r   r         Top_pointA_and_Br
      )r   r   r   r   r   r   r   r@   )r   r   r   r   r   r@   r   r   )r   r   r   r   r   r   r@   r   )r   r   r   r   r   r   r   r         GJ)linear_solver),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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_qdrR   rS   ZkindiffsZqdotsZF_COIJZI_C_COr5   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   r2   r0   r     test_linearize_rolling_disc_kane   s   "&

&&
.

 *H,L.&& 0
rq   c                  C   s2  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sJ |tg ksJ d S )Nr[   rd   r@   L, m, t皙#@r#   N*r   r%   axisr*   pP)q_indu_indr6   T)r?   r
   皙#)r   r   r   r   rN   rF   rG   rK   rJ   rH   rO   r   r   r   rQ   rV   r   )r[   rd   r_   LrX   r   rY   r#   pNr%   r*   rv   kdeRrk   rl   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sJ |tg ksJ |j|||gdddd\}}}| td	dgd| d	ggksJ |tg ks(J |j|||gdddd d\}}}| td	dgd| d	ggksLJ |tg ksUJ d S )Nq1:3r@   levelzu1:3rr   rs   r#   rt   r   r%   ru   P1rv   )rw   rx   r7   r9   r8   r:   Zacceleration_constraintsr6   Tr=   ry   rD   )r>   r?   r
   rE   c                 S   
   |  |S NZLUsolver%   br   r   r    <lambda>   s   
 z9test_linearize_pendulum_kane_nonminimal.<locals>.<lambda>)r   r   r   r   rN   r   rF   rG   rJ   rH   rI   r   r   r   rL   rM   rP   Z	magnituder,   Zexpressr   r
   r   r   rQ   rV   expand) r[   r\   r_   r`   rd   re   rg   rh   rz   rX   r   rY   r#   r{   theta1r%   r*   rv   r|   Zdq_dictrR   rS   rT   r}   rk   rl   r~   rn   ro   rp   r'   r   r   r   r    'test_linearize_pendulum_kane_nonminimal   sb   
$&&r   c                  C   sx  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sJ |tg ksJ |j| g|gddd\}}}t|tddgdt|  | dggksJ |tg ksJ d S )Nr[   r@   rr   rs   r#   rt   r   r%   ru   r*   rv   )	forcelistframeT)r?   ry   rD   )r?   rE   )r   r   r   r   rN   rF   rG   rK   rJ   rH   rO   r   r   r   form_lagranges_equationsrV   r
   r   r   )r[   r_   rz   rX   r   rY   r#   r{   r%   r*   rv   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sJ |tg ksJ |j|g|g| g|g|ddd d\}}}t|tddgd| dggksJ |tg ksJ d S )Nr   r@   r   rr   rs   r#   rt   r   r%   ru   r   rv   r3   )Z
hol_coneqsr   r   )r>   T)r>   r?   ry   c                 S   r   r   r   r   r   r   r    r   L  s   
z=test_linearize_pendulum_lagrange_nonminimal.<locals>.<lambda>)r>   r?   rE   )r   r   r   r   rN   r   rF   rG   rJ   rH   rI   rL   rM   r   r   r   r   r   r   Zsolve_multipliersupdaterV   r
   )r[   r\   r_   r`   rz   rX   r   rY   r#   r{   r   r%   r*   rv   rR   r   r   r>   Zlam_opr'   r   r   r   r    +test_linearize_pendulum_lagrange_nonminimal)  s:   
&(
$$r   c                  C   s  t d \} }}}t dd \}}}}td\}}	}
td}|dd| |jg}|dd||jg}|dd||jg}td	}||d
 |	d||j }|
||| t||	d |d  |	d |d  |	d |d  }td|||	||f}|	 |
 | t| |_t||}t||}|  | d
|d
|d
|d
|d
| d
| d
| d
i}|j|||ddd
 }tg dg dg dd
d
d
d
d| d
gd
d|
 d|  d
d| d d
d
gg dg}||ksJ d S )Nzq1 q2 q3r@   zr m gr#   Yr&   rz   r}   r(   r   Dmcr4   r3   BodyDT)rw   Zqd_indr>   r?   )r   r   r   r@   r   r   )r   r   r   r   r@   r   )r   r   r   r   r   r@   ir;   r<   )r   r   r   r   r   r   )r   r   r   rF   rG   rH   rI   r   rN   rJ   rO   r   r   r   Zpotential_energyr   r   r   r   rV   r   )r[   r\   r]   r^   r_   r`   ra   rb   rW   rX   rY   r#   r   rz   r}   r(   r   ri   r   r   lr>   r%   rm   r   r   r    $test_linearize_rolling_disc_lagrangeQ  s<   2

"r   N)"Zsympyr   r   r   r   r   r   r   Zsympy.core.sympifyr	   Zsympy.simplify.simplifyr
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