ó ~9­\c@sPdZddlmZddljjZdeed„Z de ed„Z dS(sOThis module contains some sample symbolic models used for testing and examples.iÿÿÿÿ(tbackendNicCs¢tjdj|ƒƒ}tjdj|ƒƒ}tjdj|ƒƒ}tjdƒ}tjdj|ƒƒ}tjdj|ƒƒ}tjdj|ƒƒ} tjdƒ} tjd ƒ} | j| d ƒ| g} g} g}g}x‚t|ƒD]t}| d j d j|ƒ||| j ƒ}|j| | d j | ƒ||| j ƒ| j |ƒtj d j|ƒ|||ƒ}| j ||||jƒƒ|| ||||||}y:|||d||d||d||d7}Wntk rnX|r+||||7}n|rB|| |7}n|j ||| j fƒ|j |ƒqõWtj| d|d|d| ƒ}|j||ƒ|S(sqReturns 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. sm:{}sk:{}sc:{}tgsx:{}sv:{}sf:{}tNtoriginiiÿÿÿÿscenter{}sblock{}itq_indtu_indtkd_eqs(tsmtsymbolstformattmetdynamicsymbolstReferenceFrametPointtset_veltranget locatenewtxtveltappendtParticletdifft IndexErrort KanesMethodtkanes_equations(tnt apply_gravitytapply_external_forcestmasst stiffnesstdampingtacceleration_due_to_gravityt coordinatestspeedst specifiedstceilingRtpointstkinematic_equationst particlestforcestitcentertblockt total_forcetkane((s=lib/python2.7/site-packages/sympy/physics/mechanics/models.pytmulti_mass_spring_damper sN,  "   cCsI|dkrtdƒ‚ntjdj|dƒƒ}tjdj|dƒƒ}|tkr~tjdj|dƒƒ}ntjdj|dƒƒ}tjdj|ƒƒ}tjd ƒ\}} tjd ƒ} tjd ƒ} | j | dƒtjd ƒ} | j | |d| j ƒ| j | |d| j ƒtj d | |dƒ} | g}| g}| g}| |d || j fg}|dj| ƒ|dg}|tksÃ|tkrÌg}nd}xút|ƒD]ì}| jdj|ƒd||d| jgƒ}|j| ||d| jƒ|j|ƒ|djdj|dƒ|||j ƒ}|j|d| |ƒ|j|ƒtj dt|dƒ|||dƒ}|j|ƒ|j|||d || j fƒ|tkr¡|j||ƒ|dkr<|j| || | jfƒn||dkrm|j|||| jfƒq¡|j|||| j||d| jfƒn|j||dj| ƒ||dƒqßW|tkrtjdƒ}|j| || j fƒ|j|ƒntj| d|d|d|ƒ}|j||ƒ|S(s*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. is/The number of links must be a positive integer.sq:{}isu:{}sT1:{}sm:{}sl:{}sg ttItOtP0tPa0sB{}tAxisiÿÿÿÿsP{}tPatFRRRN(t ValueErrorR R R tTrueRRR R Rtset_posRRtyRtNoneRt orientnewtzt set_ang_velRRt v2pt_theorytstrRR(Rt cart_forcet joint_torquestqtutTtmtlRttR.R/R0R1tframesR$R&R'tkindiffst specifiedR(tBitPitPaiR4R,((s=lib/python2.7/site-packages/sympy/physics/mechanics/models.pytn_link_pendulum_on_cartpsb.      / . + '  "!4. !( t__doc__t sympy.coreRRtsympy.physics.mechanicstphysicst mechanicsR tFalseR-R6RM(((s=lib/python2.7/site-packages/sympy/physics/mechanics/models.pyts  c