U —9%e?ã@s:dZddlmZddlmmZd dd„Zd d d „Z dS) zOThis module contains some sample symbolic models used for testing and examples.é)ÚbackendNéFc Cst d |¡¡}t d |¡¡}t d |¡¡}t d¡}t d |¡¡}t d |¡¡}t d |¡¡} t d¡} t d ¡} |  | d ¡| g} g} g}g}t|ƒD]<}| d   d  |¡||| j ¡}| | | d   | ¡||| j ¡|   |¡t  d  |¡|||¡}|   |||| ¡¡|| ||||||}z8|||d||d||d||d7}Wntk ršYnX|r²||||7}|rÄ|| |7}|  ||| j f¡|  |¡q¤tj| ||| d}| ||¡|S)asReturns a system containing the symbolic equations of motion and associated variables for a simple multi-degree of freedom point mass, spring, damper system with optional gravitational and external specified forces. For example, a two mass system under the influence of gravity and external forces looks like: :: ---------------- | | | | g \ | | | V k0 / --- c0 | | | | x0, v0 --------- V | m0 | ----- --------- | | | | | \ v | | | k1 / f0 --- c1 | | | | x1, v1 --------- V | m1 | ----- --------- | f1 V Parameters ========== n : integer The number of masses in the serial chain. apply_gravity : boolean If true, gravity will be applied to each mass. apply_external_forces : boolean If true, a time varying external force will be applied to each mass. Returns ======= kane : sympy.physics.mechanics.kane.KanesMethod A KanesMethod object. úm:{}zk:{}zc:{}Úgzx:{}zv:{}zf:{}ÚNÚoriginréÿÿÿÿzcenter{}zblock{}r©Zq_indZu_indZkd_eqs)ÚsmÚsymbolsÚformatÚmeÚdynamicsymbolsÚReferenceFrameÚPointÚset_velÚrangeÚ locatenewÚxZvelÚappendÚParticleÚdiffÚ IndexErrorÚ KanesMethodÚkanes_equations)ÚnZ apply_gravityZapply_external_forcesZmassZ stiffnessZdampingZacceleration_due_to_gravityZ coordinatesZspeedsZ specifiedsZceilingrÚpointsZkinematic_equationsÚ particlesÚforcesÚiÚcenterÚblockZ total_forceÚkane©r#ú]/var/www/html/Darija-Ai-API/env/lib/python3.8/site-packages/sympy/physics/mechanics/models.pyÚmulti_mass_spring_damper sX.     ÿ ÿ ÿÿ    ÿ r%TcCs<|dkrtdƒ‚t d |d¡¡}t d |d¡¡}|dkrTt d |d¡¡}t d |d¡¡}t d  |¡¡}t d ¡\}} t d ¡} t d ¡} |  | d¡t d ¡} |   | |d| j ¡|  | |d| j ¡t  d| |d¡} | g}| g}| g}| |d || j fg}|d  | ¡|dg}|dksF|dkrLg}nd}t|ƒD]Œ}|  d |¡d||d| jg¡}| | ||d| j¡| |¡|d d |d¡|||j ¡}| |d| |¡| |¡t  dt|dƒ|||d¡}| |¡| |||d || j f¡|dkrÀ| ||¡|dkrn| | || | jf¡||dkr–| |||| jf¡n*| |||| j||d| jf¡| ||d  | ¡||d¡qX|dkrt d¡}| | || j f¡| |¡tj| |||d}| ||¡|S)a-Returns the system containing the symbolic first order equations of motion for a 2D n-link pendulum on a sliding cart under the influence of gravity. :: | o y v \ 0 ^ g \ | --\-|---- | \| | F-> | o --|---> x | | --------- o o Parameters ========== n : integer The number of links in the pendulum. cart_force : boolean, default=True If true an external specified lateral force is applied to the cart. joint_torques : boolean, default=False If true joint torques will be added as specified inputs at each joint. Returns ======= kane : sympy.physics.mechanics.kane.KanesMethod A KanesMethod object. Notes ===== The degrees of freedom of the system are n + 1, i.e. one for each pendulum link and one for the lateral motion of the cart. M x' = F, where x = [u0, ..., un+1, q0, ..., qn+1] The joint angles are all defined relative to the ground where the x axis defines the ground line and the y axis points up. The joint torques are applied between each adjacent link and the between the cart and the lower link where a positive torque corresponds to positive angle. rz/The number of links must be a positive integer.zq:{}rzu:{}TzT1:{}rzl:{}zg tÚIÚOÚP0ÚPa0NzB{}ZAxisrzP{}ZPaÚFr )Ú ValueErrorr rr r r rrrZset_posrrÚyrrZ orientnewÚzZ set_ang_velrrZ v2pt_theoryÚstrrr)rZ cart_forceZ joint_torquesÚqÚuÚTÚmÚlrÚtr&r'r(r)ÚframesrrrZkindiffsZ specifiedrZBiÚPiZPair*r"r#r#r$Ún_link_pendulum_on_cartpsb1    " $ " "  *(    r7)rFF)rTF) Ú__doc__Z sympy.corerr Zsympy.physics.mechanicsZphysicsZ mechanicsr r%r7r#r#r#r$Ús  ÿ f