U
    L?hÏ(  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( $dd	e e(j)g¡Z*dd„ Z+dd„ Z,dd„ Z-dd„ Z.dd„ Z/dd„ Z0dd„ Z1dd„ Z2dd„ Z3dd„ Z4d d!„ Z5d"S )#é    )ÚsinÚcosÚtanÚpiÚsymbolsÚMatrixÚSÚFunction)ÚParticleÚPointÚReferenceFrameÚ	RigidBody)	Úangular_momentumÚdynamicsymbolsÚkinetic_energyÚlinear_momentumÚouterÚpotential_energyÚmsubsÚfind_dynamicsymbolsÚ
Lagrangian)Úcenter_of_massÚ_validate_coordinatesÚ_parse_linear_solver)ÚraisesÚwarns_deprecated_sympyzq1 q2 q3 q4 q5ÚNÚAZAxisÚBÚCc                     s¼   t dƒ‰tdƒ} |  ˆdˆj ¡ tˆjˆjƒ}td| ˆd|| fƒ‰ tdƒ}td|dƒ‰ˆj ˆd	ˆj ¡ t	t
‡ ‡fd
d„ƒ t	t
‡‡fdd„ƒ tˆˆ ˆƒd	ˆj dˆj  ks¸t‚d S )Nr   ÚAcé   r   é   ÚPÚPaé   é
   c                      s   t ˆ ˆ ˆƒS ©N©r   © ©r   r$   r)   ú^/var/www/html/venv/lib/python3.8/site-packages/sympy/physics/mechanics/tests/test_functions.pyÚ<lambda>   ó    z&test_linear_momentum.<locals>.<lambda>c                      s   t ˆ ˆ ˆƒS r'   r(   r)   ©r   r$   r)   r+   r,      r-   iô  )r   r   Úset_velÚyr   Úxr   r
   Úpointr   Ú	TypeErrorr   ÚAssertionError)r    ÚIr#   r)   ©r   r   r$   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sþt‚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s‚t‚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$   r   é   c                      s   t ˆˆˆ ˆƒS r'   ©r   r)   r6   r)   r+   r,   7   r-   z;test_angular_momentum_and_linear_momentum.<locals>.<lambda>c                      s   t ˆˆˆ ˆƒS r'   r<   r)   )r   r:   r$   r)   r+   r,   8   r-   c                      s   t ˆˆ ˆˆƒS r'   r<   r)   )r   r:   r$   r)   r+   r,   9   r-   é   N)r   r   r   r   Ú	locatenewr1   r/   Úset_ang_velÚzÚv2pt_theoryr
   r   r   r0   r   r4   r   r3   r   )	ÚmÚMÚlr5   r8   r9   r    r#   Úexpectedr)   )r   r   r:   r$   r+   Ú)test_angular_momentum_and_linear_momentum#   s(    "(*rF   c            	         sB  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s>t‚d S )Nzm M l1r8   r   r:   r   r    r#   r9   r$   r   c                      s   t ˆˆˆ ƒS r'   ©r   r)   r*   r)   r+   r,   M   r-   z%test_kinetic_energy.<locals>.<lambda>c                      s   t ˆˆˆ ƒS r'   rG   r)   )r   r   r)   r+   r,   N   r-   r;   )r   r   r   r   r/   r1   r>   r?   r@   rA   r
   r   r   r   r3   r   Úexpandr4   )	rB   rC   Úl1r8   r:   r    r#   r9   r5   r)   r6   r+   Útest_kinetic_energy>   s*    "ÿ
ÿrJ   c                  C   s  t dƒ\} }}}}}tdƒ}tdƒ}tdƒ}| |d|j ¡ | d||j ¡}	|	 d||j ¡}
tdƒ}| |||j ¡ |	 	|||¡ |
 	|||¡ t
d	|
| ƒ}t|j|jƒ}td
|	||||	fƒ}| | | |_|| | |_t||ƒ| | | || |  ks
t‚d S )Nzm M l1 g h Hr8   r   r:   r   r    r#   r9   r$   r   )r   r   r   r   r/   r1   r>   r?   r@   rA   r
   r   r   r   r4   )rB   rC   rI   ÚgÚhÚHr8   r   r:   r    r#   r9   r$   r5   r   r)   r)   r+   Útest_potential_energyS   s"    rN   c            	         s
  t dƒ\} }}}tdƒ‰tdƒ}| ˆdˆj ¡ | ddˆj ¡}| ˆdˆj ¡ td|dƒ‰| d	d
ˆj ¡}| ˆdˆj ¡ tdƒ}| ˆdˆj	 ¡ t
ˆj	ˆj	ƒ}td||d||fƒ‰ || | ˆ_| | | ˆ _tt‡ ‡fdd„ƒ tt‡‡fdd„ƒ d S )NzM m g hr   r:   r   r#   r%   r&   r$   r    r;   é   r9   r   r"   c                      s   t ˆ ˆ ˆƒS r'   ©r   r)   r*   r)   r+   r,   w   r-   z!test_Lagrangian.<locals>.<lambda>c                      s   t ˆ ˆ ˆƒS r'   rP   r)   r.   r)   r+   r,   x   r-   )r   r   r   r/   r1   r>   r
   r0   r?   r@   r   r   r   r   r3   )	rC   rB   rK   rL   r:   r#   r    r9   r5   r)   r6   r+   Útest_Lagrangiang   s"    rQ   c                  C   sˆ  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s¤t‚t|| ƒt|| ƒ || ¡   }|d|t	d | ¡ di}t||dd|d ksút‚t
dƒ}||j ||j  }	||j|jB  ||j|jB   }
d|j }d|j|jB  }|d|di}t|	|ƒ|kspt‚t|
|ƒ|ks„t‚d S )	Núa, búx, y, zr%   r   r;   T)Zsmartr   )r   r   r   Údiffr   r   r4   r   r   r   r   r1   r0   )r9   Úbr1   r0   r@   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s†t‚|||g}| ¡ | ¡  ¡ | ¡ h}t||d|ks¾t‚tdƒ\}}	}
tdƒ}||j |	|j	  |
|j
  ‰ ||	|
h}tˆ |d|kst‚tt‡ fdd„ƒ d S )	NrR   rS   )Úexcludezd, e, fr   )Zreference_framec                      s   t ˆ ƒS r'   )r   r)   ©rY   r)   r+   r,   ¦   r-   z*test_find_dynamicsymbols.<locals>.<lambda>)r   r   r   rT   r   r   r4   r   r1   r0   r@   r   Ú
ValueError)r9   rU   r1   r0   r@   rV   rW   Zexclude_listrZ   ÚeÚfr   r)   r]   r+   Útest_find_dynamicsymbols“   s     ÿ 

ra   c               
   C   sv  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srt‚d S )Nr9   rB   T)ÚrealÚp1Zp1_ptÚp2Zp2_ptr;   Úp3Zp3_pté   Úp4Zp4_ptÚb_fÚb_cmÚmbrU   ÚorO   é   r   )r   r   r
   r   r   ZOner   r   r1   r2   Zset_posr0   Ú
masscenterr@   r   Zpos_fromr4   )r9   rB   rc   rd   re   rg   rh   ri   rj   rU   Zpoint_orV   r)   r)   r+   Útest_center_of_mass¬   s$    Jrn   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 ©NTrr   rt   r)   )ru   rv   Úq3rw   rx   r)   r+   r,   Ð   s     ÿc                      s   t ˆ ˆˆgˆ ˆˆgddS rz   rt   r)   )ru   rv   r{   rx   ry   r)   r+   r,   Ò   s     ÿ)rs   rp   c                      s    t ˆ ˆˆgˆˆˆgˆˆˆgdS ©Nro   rt   r)   ©ru   rv   r{   rw   rx   ry   Úua2Úua3r)   r+   r,   Ö   s     ÿc                      s    t ˆ ˆˆgˆˆˆgˆ ˆˆgdS r|   rt   r)   r}   r)   r+   r,   Ø   s     ÿc                      s    t ˆ ˆˆgˆˆˆgˆˆˆgdS r|   rt   r)   )ru   rv   r{   rw   rx   ry   Úua1r~   r)   r+   r,   Ú   s     ÿ©Úis_dynamicsymbolsc                      s   t ˆ ˆ ˆgƒS r'   rt   r)   )ru   rv   r{   r)   r+   r,   Þ   r-   r   c                      s   t ˆˆ ˆgdˆˆgddS ©Nr   Tr   rt   r)   )ru   rv   Ús1rw   rx   r)   r+   r,   à   s     ÿc                      s   t ˆˆ ˆ ˆ gdˆgddS rƒ   rt   r)   )ru   r„   Ús2Ús3rw   r)   r+   r,   ã   s     ÿ)rp   r‚   c                      s   t ˆ ˆgdS r|   rt   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'   rt   r)   ©r9   Úf1Úf2r)   r+   r,   ì   r-   c                      s   t ˆˆ ƒˆˆ ƒgdS )Nrq   rt   r)   rˆ   r)   r+   r,   í   r-   c                      s   t ˆ ˆƒˆˆƒgƒS r'   rt   r)   )r‰   rŠ   Útr)   r+   r,   ð   r-   )r   r   r   r   r^   Z_tr	   r)   r)   )r9   r‰   rŠ   ru   rv   r{   r„   r…   r†   r‹   rw   rx   ry   r€   r~   r   r+   Útest_validate_coordinatesÁ   sJ    ÿÿ   rŒ   c                  C   sX   t ddtdƒƒt ddtdƒƒ } }tt jƒt jks6t‚tdƒ| |ƒt  | |¡ksTt‚d S )Nrf   za:9r;   zb:6ZLU)r   r   r   ZLUsolver4   )r   rU   r)   r)   r+   Útest_parse_linear_solverô   s    "r   c               	   C   s  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\t‚W 5 Q R X tƒ ^ |d|j|j |ƒ|j|jB |j|jB  d|j	|j	B   |j|jB  |j|jB  ksÆt‚W 5 Q R X t
dƒ}tƒ 4 |d|j	 |ƒ|jd|j |j	 fgkst‚W 5 Q R X d S )Nr   )ÚinertiaÚinertia_of_point_massÚgravityr   r%   r;   r#   éþÿÿÿ)Ú!sympy.physics.mechanics.functionsrŽ   r   r   r   r   r1   r0   r4   r@   r
   rm   Zmass)rŽ   r   r   r   Úpr)   r)   r+   Útest_deprecated_moved_functionsú   s    B&
ÿ
ÿÿr”   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   ru   rv   r{   Zq4Zq5r   Z	orientnewr@   r   r1   r   r0   r   r7   rF   rJ   rN   rQ   r[   ra   rn   rŒ   r   r”   r)   r)   r)   r+   Ú<module>   s(   (,3