o
    *ήc2.                     @   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            ;         sv  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 d S )%Nz	t r m g vzq1:7c                       g | ]}|  qS  diff).0qitr   S/tmp/pip-target-vg8gfxp4/lib/python/sympy/physics/mechanics/tests/test_linearize.py
<listcomp>       z4test_linearize_rolling_disc_kane.<locals>.<listcomp>zu:6zu1:7c                    r   r   r   )r   uir   r   r!   r"      r#   NNOAAxisBCCOPc                    s   g | ]
}t  |qS r   r   velr   uv)r%   r,   r   r!   r"   7   s    c                        g | ]}t   |qS r   )r   
ang_vel_inr/   )r*   r%   w_c_n_qdr   r!   r"   :        c                    r1   r   r-   r/   )r+   r%   	v_co_n_qdr   r!   r"   ;   r4         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   rC   )r   r   r   r   r   rC   r   r   )r   r   r   r   r   r   rC   r   )r   r   r   r   r   r   r   r         ),r   r   r   r   	orientnewzxy	locatenewr2   set_ang_velpos_fromdtset_velv2pt_theoryr   r   r   subsset_ang_accr   r   r   r   kanes_equationsto_linearizerf_cf_vf_ar   kindiffdictf_0f_1keysr   f_2f_3r   r   	linearizer   r
   r   	eigenvals);rmgvq1q2q3q4q5q6qq1dq2dq3dq4dq5dq6dqduu1u2u3u4u5u6u1du2du3du4du5du6dr&   r'   r)   w_b_n_qdrU   rV   kindiffsqdotsF_COIJI_C_COr8   BLFLKMfrfr_star
linearizersolr   q_opu_opqd_opud_opupright_nominalA_solB_solr   )r*   r+   r%   r,   r    r5   r3   r!    test_linearize_rolling_disc_kane   s   "&

&&
.

 *H,L.&& 4r   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 )Nrd   rs   rC   L, m, t皙#@r%   N*r   r'   axisr,   pP)q_indu_indr9   T)rB   r   皙#)r   r   r   r   rO   rG   rH   rL   rK   rI   rP   r   r   r   rS   r^   r   )rd   rs   rk   Lra   r    rb   r%   pNr'   r,   r   kdeRr   r   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 d S )Nq1:3rC   levelzu1:3r   r   r%   r   r   r'   r   P1r   )r   r   r:   r<   r;   r=   acceleration_constraintsr9   Tr@   r   )r   r   r   r   rO   r   rG   rH   rK   rI   rJ   r   r   r   rM   rN   rQ   	magnituder.   expressr   r   r   r   rS   r^   expand) rd   re   rk   rl   rs   rt   ry   rz   r   ra   r    rb   r%   r   theta1r'   r,   r   r   dq_dictrU   rV   rW   r   r   r   r   r   r   r   r)   r   r   r   r!   'test_linearize_pendulum_kane_nonminimal   sJ   
$r   c                  C   s   t d} t dd}td\}}}d}td}td}||d |dd	| |jg}||||j  |d
||j	 }	|	
||| td|	|}
t||
}t|| g|	|| |j	 fg|d}|  |j| g|gdd\}}}t|tddgdt|  | dggksJ |tg ksJ d S )Nrd   rC   r   r   r%   r   r   r'   r   r,   r   )	forcelistframeT)rB   r   )r   r   r   r   rO   rG   rH   rL   rK   rI   rP   r   r   r   form_lagranges_equationsr^   r	   r   r   )rd   rk   r   ra   r    rb   r%   r   r'   r,   r   LagLMr)   r   r   r   r!   (test_linearize_pendulum_lagrange_minimal   s$   

",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 d S )Nr   rC   r   r   r   r%   r   r   r'   r   r   r   r6   )
hol_coneqsr   r   )rA   T)rA   rB   r   )r   r   r   r   rO   r   rG   rH   rK   rI   rJ   rM   rN   r   r   r   r   r   r   solve_multipliersupdater^   r	   )rd   re   rk   rl   r   ra   r    rb   r%   r   r   r'   r,   r   rU   r   r   rA   lam_opr)   r   r   r   r!   +test_linearize_pendulum_lagrange_nonminimal
  s0   
&(
$r   c                  C   s  t d \} }}}t dd \}}}}td\}}	}
td}|dd| |jg}|dd||jg}|dd||jg}td	}||d
 |	d||j }|
||| t||	d |d  |	d |d  |	d |d  }td|||	||f}|	 |
 | t| |_t||}t||}|  | d
|d
|d
|d
|d
| d
| d
| d
i}|j|||ddd
 }tg dg dg dd
d
d
d
d| d
gd
d|
 d|  d
d| d d
d
gg dg}||ksJ d S )Nzq1 q2 q3rC   zr m gr%   Yr(   r   r   r*   r   Dmcr7   r6   BodyDT)r   qd_indrA   rB   )r   r   r   rC   r   r   )r   r   r   r   rC   r   )r   r   r   r   r   rC   ir>   r?   )r   r   r   r   r   r   )r   r   r   rG   rH   rI   rJ   r   rO   rK   rP   r   r   r   potential_energyr   r   r   r   r^   r   )rd   re   rf   rj   rk   rl   rm   rq   r`   ra   rb   r%   r   r   r   r*   r   r   r   r   lrA   r'   r   r   r   r!   $test_linearize_rolling_disc_lagrange+  s<   2

"r   N)#sympy.core.backendr   r   r   r   r   r   r   r	   sympy.core.sympifyr
   sympy.simplify.simplifyr   sympy.solvers.solversr   sympy.physics.mechanicsr   r   r   r   r   r   r   r   r   r   r   sympy.testing.pytestr   r   r   r   r   r   r   r   r   r   r!   <module>   s   ( 4
y%@!