Ed?<dZddlmZddlmcmZ d dZd dZ dS) zOThis module contains some sample symbolic models used for testing and examples.)backendNFcttjd|}tjd|}tjd|}tjd}tjd|}tjd|}tjd|} tjd} tjd } | | d | g} g} g}g}t|D]}| d  d |||| j z}|| | d  | ||| j zz| |tj d ||||}| ||||z || ||z||||zz } |||dz||dzz||dz||dzzzz }n#t$rYnwxYw|r||||zz }|r || |z }| ||| j zf| |tj| ||| }||||S)asReturns a system containing the symbolic equations of motion and associated variables for a simple multi-degree of freedom point mass, spring, damper system with optional gravitational and external specified forces. For example, a two mass system under the influence of gravity and external forces looks like: :: ---------------- | | | | g \ | | | V k0 / --- c0 | | | | x0, v0 --------- V | m0 | ----- --------- | | | | | \ v | | | k1 / f0 --- c1 | | | | x1, v1 --------- V | m1 | ----- --------- | f1 V Parameters ========== n : integer The number of masses in the serial chain. apply_gravity : boolean If true, gravity will be applied to each mass. apply_external_forces : boolean If true, a time varying external force will be applied to each mass. Returns ======= kane : sympy.physics.mechanics.kane.KanesMethod A KanesMethod object. m:{}zk:{}zc:{}gzx:{}zv:{}zf:{}Noriginrzcenter{}zblock{}rq_indu_indkd_eqs)smsymbolsformatmedynamicsymbolsReferenceFramePointset_velrange locatenewxvelappendParticlediff IndexError KanesMethodkanes_equations)n apply_gravityapply_external_forcesmass stiffnessdampingacceleration_due_to_gravity coordinatesspeeds specifiedsceilingr pointskinematic_equations particlesforcesicenterblock total_forcekanes >lib/python3.11/site-packages/sympy/physics/mechanics/models.pymulti_mass_spring_damperr6 s%\ :fmmA&& ' 'D 6==++,,Ijq))**G"$*S//#FMM!$4$455K  v}}Q// 0 0F"6==#3#344J$$G Xh  F NN7AXFI F 1XX  %%j&7&7&:&:&1!nwy&@BBwr w 7 7ay79,!- . . . f I,,Q//aAA""6!9{1~/B/B/D/D#DEEE!! }{1~5qzF1I-.   Ia!e,{1q5/AA#AENVAE]:; 'F!4 6 6 6DF+++ Ks42J'' J43J4Tc |dkrtdtjd|dz}tjd|dz}|dur*tjd|dz}t jd|dz}t jd |}t jd \}} tjd } tjd } | | dtjd } | | |d| j z| | |d| j ztj d| |d} | g}| g}| g}| |d |z| j zfg}|d | |dz g}|dus|durg}nd}t|D]N}| d|d||dz| jg}|| ||dz| jz|||dd|dz|||j z}||d| |||tj dt+|dzz|||dz}||||||dz |z| j zf|dur||||dkr&|| || | jzf||dz kr&||||| jzfn9||||| jz||dz| jzz f|||dz | ||dzz P|durHtjd}|| || j zf||tj| |||}||||S)a-Returns the system containing the symbolic first order equations of motion for a 2D n-link pendulum on a sliding cart under the influence of gravity. :: | o y v \ 0 ^ g \ | --\-|---- | \| | F-> | o --|---> x | | --------- o o Parameters ========== n : integer The number of links in the pendulum. cart_force : boolean, default=True If true an external specified lateral force is applied to the cart. joint_torques : boolean, default=False If true joint torques will be added as specified inputs at each joint. Returns ======= kane : sympy.physics.mechanics.kane.KanesMethod A KanesMethod object. Notes ===== The degrees of freedom of the system are n + 1, i.e. one for each pendulum link and one for the lateral motion of the cart. M x' = F, where x = [u0, ..., un+1, q0, ..., qn+1] The joint angles are all defined relative to the ground where the x axis defines the ground line and the y axis points up. The joint torques are applied between each adjacent link and the between the cart and the lower link where a positive torque corresponds to positive angle. rz/The number of links must be a positive integer.zq:{}rzu:{}TzT1:{}rzl:{}zg tIOP0Pa0NzB{}Axisr zP{}PaFr ) ValueErrorrrrrrrrrset_posrryrr orientnewz set_ang_velrr v2pt_theorystrrr )r! cart_force joint_torquesquTmlrtr8r9r:r;framesr,r.r/kindiffs specifiedr0BiPiPair>r4s r5n_link_pendulum_on_cartrUpsb AvLJKKK &--A..//A &--A..//A5  gnnQU33 4 4 6==Q''((A 6==##$$A :e  DAq #A  AIIaOOO $BJJq!A$*JJq!A$* +eR1 & &CSFTFIAaD519qs?# $F! ! qt#$HT]d2  1XX55 [[a&1QU8QS/ B B q!AE(QS.))) b BZ ! !%,,q1u"5"5qtbd{ C C vbz1b))) bk$QU+R1q5:: rAa!eH9q=13./000 D A   QqT " " "Av 0 q1Q4%!#+.///AEz A r1Q4!#:.//// r1Q4!#:!a%13#>?@@@!a% a((1QU834444T  c " " r1qs7m$$$ >!1Ah ? ? ?DF+++ K)rFF)rTF) __doc__ sympy.corerrsympy.physics.mechanicsphysics mechanicsrr6rUrVr5r]s  %$$$$$$$$$$$$$$1638ccccLvvvvvvrV