\h?>SrSSKJr SSKJs Jr SSjrSSjr g)zOThis module contains some sample symbolic models used for testing and examples.)backendNc[R"SRU55n[R"SRU55n[R"SRU55n[R"S5n[R"SRU55n[R"SRU55n[R"SRU55n [R "S5n [R "S 5n U RU S 5 U /n /n /n/n[U5GHbnU S RS RU5UUU R-5nURXS RU 5UUU R--5 U RU5 [R"S RU5UUU5nU RUUUUR5- 5 UU*UU-UUUU-- nUUUS-UUS--UUS-UUS---- nU(a UUUU-- nU(aUU U- nURUUU R-45 URU5 GMe [R "XUU S9nUR#X5 U$![a Nf=f)aReturns a system containing the symbolic equations of motion and associated variables for a simple multi-degree of freedom point mass, spring, damper system with optional gravitational and external specified forces. For example, a two mass system under the influence of gravity and external forces looks like: :: ---------------- | | | | g \ | | | V k0 / --- c0 | | | | x0, v0 --------- V | m0 | ----- --------- | | | | | \ v | | | k1 / f0 --- c1 | | | | x1, v1 --------- V | m1 | ----- --------- | f1 V Parameters ========== n : integer The number of masses in the serial chain. apply_gravity : boolean If true, gravity will be applied to each mass. apply_external_forces : boolean If true, a time varying external force will be applied to each mass. Returns ======= kane : sympy.physics.mechanics.kane.KanesMethod A KanesMethod object. m:{}zk:{}zc:{}gzx:{}zv:{}zf:{}Noriginrzcenter{}zblock{}q_indu_indkd_eqs)smsymbolsformatmedynamicsymbolsReferenceFramePointset_velrange locatenewxvelappendParticlediff IndexError KanesMethodkanes_equations)n apply_gravityapply_external_forcesmass stiffnessdampingacceleration_due_to_gravity coordinatesspeeds specifiedsceilingrpointskinematic_equations particlesforcesicenterblock total_forcekanes V/var/www/auris/envauris/lib/python3.13/site-packages/sympy/physics/mechanics/models.pymulti_mass_spring_damperr6 s\ ::fmmA& 'D 6==+,Ijjq)*G"$**S/##FMM!$45K   v}}Q/ 0F""6==#34J$G XXh F NN7AXFI F 1X%%j&7&7&:&1!nwyy&@Bwr w 7ay799,!- . f I,,Q/aA""6!9{1~/B/B/D#DE!! }{1~5qzF1I-.   Ia!e,{1q5/AA#AENVAE]:; >'F!4 6D+ K#   s1&K K$#K$cUS::a [S5e[R"SRUS-55n[R"SRUS-55nUSLa([R"SRUS-55n[R "SRUS-55n[R "S RU55n[R "S 5up[R "S 5n [R"S 5n U RU S5 [R"S 5n U RXSU R-5 U RXSU R-5 [R"SXS5n U /nU /nU /nXS*U-U R-4/nUSRU 5US- /nUSLdUSLa/nOSn[U5GH nU RSRU5SUUS-U R /5nUR#XUS-U R -5 UR%U5 USR'SRUS-5UUUR-5nUR)USU U5 UR%U5 [R"S[+US-5-UUUS-5nUR%U5 UR%UUUS-*U-U R-45 USLaUR%WU5 US:Xa#UR%XU*U R -45 UUS- :Xa$UR%UUUU R -45 O9UR%UUUU R -UUS-U R -- 45 UR%UUS-RU 5UUS-- 5 GM USLaG[R"S5nUR%U UU R-45 UR%U5 [R,"XUUS9nUR/UU5 U$)aReturns 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:{}r zu:{}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 AvJKK &--A./A &--A./A   gnnQU3 4 6==Q'(A 6==#$A ::e DA #A  AIIaO $BJJqA$*JJqA$* ++eR1 &CSFTFIaD519qss?# $F! ! qt#$HT]d2  1X [[a&1QU8QSS/ B qAE(QSS.) b BZ ! !%,,q1u"5qtbdd{ C vbz1b) bkk$QU+R1q5: rAa!eH9q=133./0 D   QqT "Av qQ4%!##+./AEz r1Q4!##:./ r1Q4!##:!a%133#>?@!a% a(1QU83458T   c " r1qss7m$ >>!Ah ?DF+ K)r FF)r TF) __doc__ sympy.corerrsympy.physics.mechanicsphysics mechanicsrr6rUrVr5r]s* %$$1638cLvrV