o
    GZŽhÏ(  ã                   @   sB  d dl mZmZmZmZmZmZmZmZ d dl	m
Z
mZmZmZ d dl	mZmZmZmZmZmZmZmZmZ d dlmZmZmZ d dlmZmZ edƒ\ZZZ Z!Z"edƒZ#e# $dd	ee#j%g¡Z&e& $d
d	ee&j'g¡Z(e( $dd	e e(j)g¡Z*dd„ Z+dd„ Z,dd„ Z-dd„ Z.dd„ Z/dd„ Z0dd„ Z1dd„ Z2dd„ Z3dd„ Z4d d!„ Z5d"S )#é    )ÚsinÚcosÚtanÚpiÚsymbolsÚMatrixÚSÚFunction)ÚParticleÚPointÚReferenceFrameÚ	RigidBody)	Úangular_momentumÚdynamicsymbolsÚkinetic_energyÚlinear_momentumÚouterÚpotential_energyÚmsubsÚfind_dynamicsymbolsÚ
Lagrangian)Úcenter_of_massÚ_validate_coordinatesÚ_parse_linear_solver)ÚraisesÚwarns_deprecated_sympyzq1 q2 q3 q4 q5ÚNÚAZAxisÚBÚCc                     s¼   t dƒ‰tdƒ} |  ˆdˆj ¡ tˆjˆjƒ}td| ˆd|| fƒ‰ tdƒ}td|dƒ‰ˆj ˆd	ˆj ¡ t	t
‡ ‡fd
d„ƒ t	t
‡‡fdd„ƒ tˆˆ ˆƒd	ˆj dˆj  ks\J ‚d S )Nr   ÚAcé   r   é   ÚPÚPaé   é
   c                      ó   t ˆ ˆ ˆƒS ©N©r   © ©r   r$   r*   ú[/var/www/auris/lib/python3.10/site-packages/sympy/physics/mechanics/tests/test_functions.pyÚ<lambda>   ó    z&test_linear_momentum.<locals>.<lambda>c                      r'   r(   r)   r*   ©r   r$   r*   r,   r-      r.   iô  )r   r   Úset_velÚyr   Úxr   r
   Úpointr   Ú	TypeErrorr   )r    ÚIr#   r*   ©r   r   r$   r,   Útest_linear_momentum   s   (r7   c            	   	      s„  t dƒ\} }}}tdƒ}tdƒ‰tdƒ}tdƒ‰ˆ d|ˆj ¡}| d|ˆj ¡}ˆ ˆdˆj ¡ | ˆ|ˆj ¡ | 	ˆˆ|¡ | 	ˆˆ|¡ t
d	|| ƒ‰td
||||tˆjˆjƒ |fƒ‰ d|  | | ˆj || | ˆj  }tˆˆ ˆƒ|ksJ ‚tt‡ ‡‡fdd„ƒ tt‡ ‡‡fdd„ƒ tt‡‡‡fdd„ƒ |||d   d|  |d   | ˆj }tˆˆˆ ˆƒ|ksÀJ ‚dS )a   A rod with length 2l, centroidal inertia I, and mass M along with a
    particle of mass m fixed to the end of the rod rotate with an angular rate
    of omega about point O which is fixed to the non-particle end of the rod.
    The rod's reference frame is A and the inertial frame is N.z
m, M, l, IÚomegar   ÚaÚOr    r#   r   r$   r   é   c                      ó   t ˆˆˆ ˆƒS r(   ©r   r*   r6   r*   r,   r-   7   ó    z;test_angular_momentum_and_linear_momentum.<locals>.<lambda>c                      r<   r(   r=   r*   )r   r:   r$   r*   r,   r-   8   r>   c                      s   t ˆˆ ˆˆƒS r(   r=   r*   )r   r:   r$   r*   r,   r-   9   r>   é   N)r   r   r   r   Ú	locatenewr2   r0   Úset_ang_velÚzÚv2pt_theoryr
   r   r   r1   r   r   r4   r   )	ÚmÚMÚlr5   r8   r9   r    r#   Úexpectedr*   )r   r   r:   r$   r,   Ú)test_angular_momentum_and_linear_momentum#   s(   "(*rH   c            	         s@  t dƒ\} }}tdƒ}tdƒ‰tdƒ}| ˆdˆj ¡ | d|ˆj ¡}| d|ˆj ¡}tdƒ}| ˆ|ˆj ¡ | 	|ˆ|¡ | 	|ˆ|¡ t
d	|| ƒ‰tˆjˆjƒ}td
|||||fƒ‰ tt‡ ‡fdd„ƒ tt‡ ‡fdd„ƒ dtˆˆˆ ƒ||d  |d  d d|d  |  |d   |d d    ¡ ksžJ ‚d S )Nzm M l1r8   r   r:   r   r    r#   r9   r$   r   c                      ó   t ˆˆˆ ƒS r(   ©r   r*   r+   r*   r,   r-   M   r.   z%test_kinetic_energy.<locals>.<lambda>c                      rI   r(   rJ   r*   )r   r   r*   r,   r-   N   r.   r;   )r   r   r   r   r0   r2   r@   rA   rB   rC   r
   r   r   r   r4   r   Úexpand)	rD   rE   Úl1r8   r:   r    r#   r9   r5   r*   r6   r,   Útest_kinetic_energy>   s.   "ÿ
ÿÿrM   c                  C   s  t dƒ\} }}}}}tdƒ}tdƒ}tdƒ}| |d|j ¡ | d||j ¡}	|	 d||j ¡}
tdƒ}| |||j ¡ |	 	|||¡ |
 	|||¡ t
d	|
| ƒ}t|j|jƒ}td
|	||||	fƒ}| | | |_|| | |_t||ƒ| | | || |  ks„J ‚d S )Nzm M l1 g h Hr8   r   r:   r   r    r#   r9   r$   r   )r   r   r   r   r0   r2   r@   rA   rB   rC   r
   r   r   r   )rD   rE   rL   ÚgÚhÚHr8   r   r:   r    r#   r9   r$   r5   r   r*   r*   r,   Útest_potential_energyS   s"   *rQ   c            	         s
  t dƒ\} }}}tdƒ‰tdƒ}| ˆdˆj ¡ | ddˆj ¡}| ˆdˆj ¡ td|dƒ‰| d	d
ˆj ¡}| ˆdˆj ¡ tdƒ}| ˆdˆj	 ¡ t
ˆj	ˆj	ƒ}td||d||fƒ‰ || | ˆ_| | | ˆ _tt‡ ‡fdd„ƒ tt‡‡fdd„ƒ d S )NzM m g hr   r:   r   r#   r%   r&   r$   r    r;   é   r9   r   r"   c                      r'   r(   ©r   r*   r+   r*   r,   r-   w   r.   z!test_Lagrangian.<locals>.<lambda>c                      r'   r(   rS   r*   r/   r*   r,   r-   x   r.   )r   r   r   r0   r2   r@   r
   r1   rA   rB   r   r   r   r   r4   )	rE   rD   rN   rO   r:   r#   r    r9   r5   r*   r6   r,   Útest_Lagrangiang   s"   rT   c                  C   s„  t dƒ\} }tdƒ\}}}t| | | || ¡  | g| ¡  ¡ |t| ¡ ƒ ggƒ}t| | |g| ¡  ¡ dggƒ}|d|d| ¡ d| ¡ di}t||ƒ|ksRJ ‚t|| ƒt|| ƒ || ¡   }|d|td | ¡ di}t||dd|d ks}J ‚t	dƒ}||j
 ||j  }	||j
|j
B  ||j|jB   }
d|j }d|j|jB  }|d|di}t|	|ƒ|ks·J ‚t|
|ƒ|ksÀJ ‚d S )	Núa, búx, y, zr%   r   r;   T)Zsmartr   )r   r   r   Údiffr   r   r   r   r   r   r2   r1   )r9   Úbr2   r1   rB   ÚexprÚsolÚsdr   ÚvÚdZv_solZd_solr*   r*   r,   Ú
test_msubs{   s*   ÿÿ$ 
r^   c                     s&  t dƒ\} }tdƒ\}}}t| | | || ¡  | g| ¡  ¡ |t| ¡ ƒ ggƒ}|| ¡ || ¡  ¡ || ¡ h}t|ƒ|ksCJ ‚|||g}| ¡ | ¡  ¡ | ¡ h}t||d|ks_J ‚tdƒ\}}	}
tdƒ}||j |	|j  |
|j	  ‰ ||	|
h}tˆ |d|ksˆJ ‚t
t‡ fdd„ƒ d S )	NrU   rV   )Úexcludezd, e, fr   )Zreference_framec                      s   t ˆ ƒS r(   )r   r*   ©r\   r*   r,   r-   ¦   s    z*test_find_dynamicsymbols.<locals>.<lambda>)r   r   r   rW   r   r   r   r2   r1   rB   r   Ú
ValueError)r9   rX   r2   r1   rB   rY   rZ   Zexclude_listr]   ÚeÚfr   r*   r`   r,   Útest_find_dynamicsymbols“   s    ÿ 

rd   c               
   C   st  t dƒ} tddd}tdtdƒtjƒ}tdtdƒtd	ƒƒ}td
tdƒtdƒƒ}tdtdƒ|ƒ}t dƒ}tdƒ}tdƒ}td|||t|j|jƒ|fƒ}	|j	 
|j	| j¡ |j	 
|j	| j| j ¡ |j	 
|j	| j¡ |	j 
|j	| j| j ¡ tdƒ}
|
 
|j	t|j	|||||	ƒ¡ d|| d  | j || d || d  | j  ||| d  | j  }|
 |j	¡| dks¸J ‚d S )Nr9   rD   T)ÚrealÚp1Zp1_ptÚp2Zp2_ptr;   Úp3Zp3_pté   Úp4Zp4_ptÚb_fÚb_cmÚmbrX   ÚorR   é   r   )r   r   r
   r   r   ZOner   r   r2   r3   Zset_posr1   Ú
masscenterrB   r   Zpos_from)r9   rD   rf   rg   rh   rj   rk   rl   rm   rX   Zpoint_orY   r*   r*   r,   Útest_center_of_mass¬   s$   Jrq   c                
      sÌ  t dƒ\	‰‰‰‰
‰‰‰‰‰tdƒ\‰‰‰tˆˆˆgˆ
ˆˆgˆˆˆgd tˆˆgƒ tˆˆgˆ
gƒ tˆ
ˆgd tˆˆˆgˆ
ˆˆgdd tt‡‡‡
‡‡fdd„ƒ tˆˆˆgˆ
ˆˆgdd tt‡‡‡‡
‡fd	d„ƒ tt‡‡‡‡‡fd
d„ƒ tˆˆˆgˆ
ˆˆgdˆ
ˆˆgd tt‡‡‡‡
‡‡‡‡fdd„ƒ tt‡‡‡‡
‡‡‡‡fdd„ƒ tt‡‡‡‡
‡‡‡‡fdd„ƒ tˆˆ ˆgdd tt‡‡‡fdd„ƒ tˆˆˆgdˆ
ˆgdd tt‡‡‡‡
‡fdd„ƒ tˆˆ ˆ ˆgdˆ
gdd tt‡‡‡‡‡
fdd„ƒ tˆˆgdd tt‡‡fdd„ƒ t j‰	tdƒ‰ tdtd\‰‰tˆˆ ƒˆˆ ƒgdd tt‡ ‡‡fdd„ƒ tt‡ ‡‡fdd„ƒ ˆ t _tˆˆ ƒˆˆ ƒgƒ tt‡‡‡	fdd„ƒ ˆ	t _d S )Nzq1:4 u1:4 ua1:4zs1:4©Úu_auxiliary©ZspeedsF©Úcheck_duplicatesc                      s   t ˆ ˆˆgˆˆˆgƒS r(   ©r   r*   )Úq1Úq2Úu1Úu2Úu3r*   r,   r-   Í   s    ÿz+test_validate_coordinates.<locals>.<lambda>c                      s   t ˆ ˆˆgˆˆˆgddS ©NTru   rw   r*   )rx   ry   Úq3rz   r{   r*   r,   r-   Ð   ó    ÿc                      s   t ˆ ˆˆgˆ ˆˆgddS r}   rw   r*   )rx   ry   r~   r{   r|   r*   r,   r-   Ò   r   )rv   rs   c                      s    t ˆ ˆˆgˆˆˆgˆˆˆgdS ©Nrr   rw   r*   ©rx   ry   r~   rz   r{   r|   Úua2Úua3r*   r,   r-   Ö   ó    ÿc                      s    t ˆ ˆˆgˆˆˆgˆ ˆˆgdS r€   rw   r*   r   r*   r,   r-   Ø   r„   c                      s    t ˆ ˆˆgˆˆˆgˆˆˆgdS r€   rw   r*   )rx   ry   r~   rz   r{   r|   Úua1r‚   r*   r,   r-   Ú   r„   ©Úis_dynamicsymbolsc                      s   t ˆ ˆ ˆgƒS r(   rw   r*   )rx   ry   r~   r*   r,   r-   Þ   s    r   c                      s   t ˆˆ ˆgdˆˆgddS ©Nr   Tr†   rw   r*   )rx   ry   Ús1rz   r{   r*   r,   r-   à   r   c                      s   t ˆˆ ˆ ˆ gdˆgddS rˆ   rw   r*   )rx   r‰   Ús2Ús3rz   r*   r,   r-   ã   s    ÿ)rs   r‡   c                      s   t ˆ ˆgdS r€   rw   r*   )r‰   r…   r*   r,   r-   æ   r>   r9   zf1:3)Úclsc                      s   t ˆˆ ƒˆˆ ƒgƒS r(   rw   r*   ©r9   Úf1Úf2r*   r,   r-   ì   ó    c                      s   t ˆˆ ƒˆˆ ƒgdS )Nrt   rw   r*   r   r*   r,   r-   í   s    c                      s   t ˆ ˆƒˆˆƒgƒS r(   rw   r*   )rŽ   r   Útr*   r,   r-   ð   r   )r   r   r   r   ra   Z_tr	   r*   r*   )r9   rŽ   r   rx   ry   r~   r‰   rŠ   r‹   r‘   rz   r{   r|   r…   r‚   rƒ   r,   Útest_validate_coordinatesÁ   sJ   ÿÿ   
r’   c                  C   sX   t ddtdƒƒt ddtdƒƒ} }tt jƒt jksJ ‚tdƒ| |ƒt  | |¡ks*J ‚d S )Nri   za:9r;   zb:6ZLU)r   r   r   ZLUsolve)r   rX   r*   r*   r,   Útest_parse_linear_solverô   s   ""r“   c                  C   sX  ddl m} m}m} tdƒ}tƒ $ | |ddddƒ|j|jB |j|jB  |j|jB  ks.J ‚W d   ƒ n1 s8w   Y  tƒ 4 |d|j|j |ƒ|j|jB |j|jB  d|j|jB   |j|jB  |j|jB  ksmJ ‚W d   ƒ n1 sww   Y  t	dƒ}tƒ  |d|j |ƒ|j
d|j |j fgksšJ ‚W d   ƒ d S 1 s¥w   Y  d S )Nr   )ÚinertiaÚinertia_of_point_massÚgravityr   r%   r;   r#   éþÿÿÿ)Ú!sympy.physics.mechanics.functionsr”   r•   r–   r   r   r2   r1   rB   r
   rp   Zmass)r”   r•   r–   r   Úpr*   r*   r,   Útest_deprecated_moved_functionsú   s$   :ÿ&
ÿ
ÿ
ÿÿ."ÿrš   N)6Zsympyr   r   r   r   r   r   r   r	   Zsympy.physics.mechanicsr
   r   r   r   r   r   r   r   r   r   r   r   r   r˜   r   r   r   Zsympy.testing.pytestr   r   rx   ry   r~   Zq4Zq5r   Z	orientnewrB   r   r2   r   r1   r   r7   rH   rM   rQ   rT   r^   rd   rq   r’   r“   rš   r*   r*   r*   r,   Ú<module>   s*   ( ,3