I am guessing (I have not read the code in details) that IF the NameError is raised by nsolve it means that whatever eval-ish procedure is used in nsolve it does not support `Derivative`. In other words, SymPy can not evaluate derivatives numerically and you have `Derivative`s in the expression you are feeding to nsolve. If this is correct can you try to give us only that expression?
note: Derivative is a sympy object used to store unevaluated derivatives. Usually you can just evaluate them: Derivative(2*x, x).doit() -> 2 however due to bugs or fancy substitutions you may have some of them unevaluated. On 27 January 2013 22:16, Renxian <[email protected]> wrote: >> it works ok till the first nsolver. the code is to trim an aircraft. >> >> >> >> i found some errors in my code , and the corrected one is below, >> but a new error happen, which is NameError: global name >> 'Derivative' is not defined >> >> (i have removed the first nsolve since it is ok, only left the second >> to trim an aircraft for steady turn, >> sorry i can not give an simple example) >> >> >> >> >> >> >> >> >> from sympy import * >> import numpy as np >> init_printing(use_unicode=False, wrap_line=True, no_global=True) >> #flat earth, rigid ,symatric , body axis >> theta,phi,psi=var('theta,phi,psi') >> p,q,r=var('p,q,r') >> u,v,w=var('u,v,w') >> Xe,Ye,Ze=var('Xe,Ye,Ze') >> deltAileron,deltRudder=var('deltAileron,deltRudder') >> deltFlap,deltElevator,dotAlpha=var('deltFlap,deltElevator,dotAlpha') >> fuel=var('fuel') >> omega=var('omega') >> thr=var('thr') >> #################################### >> #g=var('g') >> g=9.81#m/s**2 >> ## DCM from inerria frame to body frame >> H_I2B=Matrix([[cos(theta)*cos(psi),cos(theta)*sin(psi),-sin(theta)], >> >> [(-cos(theta)*sin(psi)+sin(phi)*sin(theta)*cos(psi)),(cos(phi)*cos(psi)+sin(phi)*sin(theta)*cos(psi)),sin(phi)*cos(theta)], >> >> [(sin(phi)*sin(psi)+cos(phi)*sin(theta)*cos(psi)),(-sin(phi)*cos(psi)+cos(phi)*sin(theta)*sin(psi)),cos(phi)*cos(theta)]]) >> >> gx,gy,gz=H_I2B*Matrix(3,1,[0,0,g])#gravity in body frame >> >> #b,c,S=var('b,c,S') >> #wing span >> b=2.8956# m >> #mean aerodynamics chord >> c=0.189941 # % >> #wing area >> S=0.55# m**2 >> #m=var('m') >> m=13.5# kg >> #e,AR=var('e,AR') >> #Oswald's coefficient >> e=0.75 >> AR=b**2/S >> >> ################ISA for Troposphere ############# >> T0=288.15 # sea level tempreture ,k (15 centigree) >> P_atm0=101325# N/m**2 >> R=287.04 #Characteristic gas constant (J/Kg/K) >> gamma=1.4 #Ratio of specific heats >> #altitude >> h=-Ze >> T=T0-6.5*h/1000 >> P_atm=P_atm0*(1-0.0065*h/T0)**5.2561 >> rho=P_atm/(R*T) >> speedofsound=(T*R*gamma)**0.5 >> ############### air data ##############33 >> >> #uw,vw,ww=var('uw,vw,ww')#wind speed >> uw=0 >> vw=0 >> ww=0 >> >> ua,va,wa=Matrix(3,1,[u,v,w])-H_I2B*Matrix(3,1,[uw,vw,ww]) >> #alpha,beta,Va,Mach=var('alpha,beta,Va,Mach') >> Va=(ua**2+va**2+wa**2)**0.5 >> alpha=atan(wa/ua) >> beta=asin(va/Va) >> Mach=Va/speedofsound >> q_bar=rho*Va**2/2 >> >> ########### aerodynamic doefficients ###################### >> >> #CL_0,CL_alpha,CL_deltFlap,CL_deltElevator,CL_dotAlpha,CL_q,CL_Mach=var('CL_0,CL_alpha,CL_deltFlap,CL_deltElevator,CL_dotAlpha,CL_q,CL_Mach') >> ####Lift coefficient###### >> #Zero-alpha lift >> CL_0=0.23 >> CL_alpha=5.6106 >> CL_deltFlap=0.74 >> CL_deltElevator=0.13 >> CL_dotAlpha=1.9724 >> CL_q=7.9543 >> CL_Mach=0 >> >> #CD_0,CL_minD,CD_deltFlap,CD_deltElevator,CD_deltAileron,CD_deltRudder,CD_Mach=var('CD_0,CL_minD,CD_deltFlap,CD_deltElevator,CD_deltAileron,CD_deltRudder,CD_Mach') >> CD_0=0.0434 >> CL_minD=0.23 >> CD_deltFlap=0.1467 >> CD_deltElevator=0.0135 >> CD_deltAileron=0.0302 >> CD_deltRudder=0.0303 >> CD_Mach=0 >> >> #CY_beta,CY_deltAileron,CY_deltRudder,CY_p,CY_r=var('CY_beta,CY_deltAileron,CY_deltRudder,CY_p,CY_r') >> CY_beta=-0.83 >> CY_deltAileron=-0.075 >> CY_deltRudder=0.1914 >> CY_p=0 >> CY_r=0 >> >> #Cm_0,Cm_alpha,Cm_deltFlap,Cm_deltElevator,Cm_dotAlpha,Cm_q,Cm_Mach=var('Cm_0,Cm_alpha,Cm_deltFlap,Cm_deltElevator,Cm_dotAlpha,Cm_q,Cm_Mach') >> Cm_0=0.135 >> Cm_alpha=-2.7397 >> Cm_deltFlap=0.0467 >> Cm_deltElevator=-0.9918 >> Cm_dotAlpha=-10.3796 >> Cm_q=-38.2067 >> Cm_Mach=0 >> >> #Cl_beta,Cl_deltAileron,Cl_deltRudder,Cl_p,Cl_r=var('Cl_beta,Cl_deltAileron,Cl_deltRudder,Cl_p,Cl_r') >> Cl_beta=-0.13 >> Cl_deltAileron=-0.1695 >> Cl_deltRudder=0.0024 >> Cl_p=-0.5051 >> Cl_r=0.2519 >> >> #Cn_beta,Cn_deltAileron,Cn_deltRudder,Cn_p,Cn_r=var('Cn_beta,Cn_deltAileron,Cn_deltRudder,Cn_p,Cn_r') >> Cn_beta=0.0726 >> Cn_deltAileron=0.0108 >> Cn_deltRudder=0.-0.0693 >> Cn_p=-0.069 >> Cn_r=-0.0946 >> >> ### in total ### >> #CL,CD,CY_w,Cm,Cl,Cn=var('CL,CD,CY,Cm,Cl,Cn') >> CL=CL_0+CL_alpha*alpha+CL_deltFlap*deltFlap+CL_deltElevator*deltElevator\ >> +(CL_dotAlpha*dotAlpha+CL_q*q)*c/(2*Va)+CL_Mach*Mach >> >> CD=CD_0+(CL-CL_minD)**2/(pi*e*AR)+CD_deltFlap*(deltFlap)+CD_deltElevator*(deltElevator)\ >> +CD_deltAileron*(deltAileron)+CD_deltRudder*(deltRudder)+CD_Mach*Mach >> >> CY_w=CY_beta*beta+CY_deltAileron*deltAileron+CY_deltRudder*deltRudder+(CY_p*p+CY_r*r)*b/(2*Va) >> Cm=Cm_0+Cm_alpha*alpha+Cm_deltFlap*deltFlap+Cm_deltElevator*deltElevator\ >> +(Cm_dotAlpha*dotAlpha+Cm_q*q)*c/(2*Va)+Cm_Mach*Mach >> >> Cl=Cl_beta*beta+Cl_deltAileron*deltAileron+Cl_deltRudder*deltRudder+(Cl_p*p+Cl_r*r)*b/(2*Va) >> >> Cn=Cn_beta*beta+Cn_deltAileron*deltAileron+Cn_deltRudder*deltRudder+(Cn_p*p+Cn_r*r)*b/(2*Va) >> H_b2w=Matrix([[cos(alpha)*cos(beta),sin(beta),sin(alpha)*cos(beta)], >> [-cos(alpha)*sin(beta),cos(beta),-sin(alpha)*sin(beta)], >> [-sin(alpha),0,cos(alpha)]]) >> #CX,CY,CZ=var('CX,CY,CZ') >> CX,CY,CZ=H_b2w.transpose()*Matrix(3,1,[-CD,CY_w,-CL]) >> >> >> ##############Fixed-pitch propeller##############333 >> >> #Jar,CT,CP=var('Jar,CT,CP') >> #propeller radius >> R_prop=0.254# m >> >> Jar=pi*Va/(omega*R_prop) >> #coefficient of thrust (CT) and power (CP) >> #the fomular is got after curve fitting using quadratic polynomial >> CT=-0.02162763*Jar**2-0.03491274*Jar+0.03787723 >> CP=-0.01860428*Jar**2-0.01512463*Jar+0.02509024 >> F_prop=4*rho*R_prop**4*omega**2*CT/pi**2 >> M_prop=-4*rho*R_prop**5*omega**2*CP >> ##################Piston engine################### >> >> MAPmin=60; >> MAP=thr*(P_atm/1000-MAPmin)+MAPmin >> RPM=omega*30/pi >> #the fomulas of fuel flow and power of piston are got using polynomial >> surface fitiing in Matlab >> >> Fuelflow=(-3189+0.2615*RPM+119.6*MAP-0.00001329*RPM**2-0.005922*RPM*MAP-1.483*MAP**2\ >> >> +3.257/10**10*RPM**3+1.377/10**7*RPM**2*MAP+0.00003562*RPM*MAP**2+0.006149*MAP**3)/1000/3600 >> >> Power_P=-10600+1.38*RPM+367.1*MAP-0.0000768*RPM**2-0.03094*RPM*MAP-4.202*MAP**2\ >> >> +3.727/10**9*RPM**3+3.917/10**7*RPM**2*MAP+0.0002021*RPM*MAP**2+0.01572*MAP**3 >> power_corrected=(T0/T)**0.5*Power_P >> M_eng=power_corrected/omega >> ###### engine total force and moment######### >> J_eng=0.001# engine shaft moment of inertia >> J_prop=0.002# propeller moment of inertia >> MomentofInertiaofEngAndProp=(M_eng+M_prop)/(J_eng+J_prop) # which is >> omega dot >> >> ######## mass,inertia and their derivatives and cg lacation >> ################# >> #empty aricraft mass >> m_empty=8.5 >> #gross aricraft mass >> m_gross=13.5 >> #empty CG location [x y z] >> cg_empty=Matrix([0.156,0,0.079]) >> #gross CG location [x y z] >> cg_gross=Matrix([0.159,0,0.090]) >> #empty moment of inertia >> Ixx_empty=0.7795 #kg*m^2 >> Iyy_empty=1.122 >> Izz_empty=1.752 >> Ixz_empty=0.1211 >> #empty inertia matrix >> I_empty=Matrix([[Ixx_empty,0,-Ixz_empty], >> [0,Iyy_empty,0], >> [-Ixz_empty,0,Izz_empty]]) >> #gross moment of inertia >> Ixx_gross=0.8244# kg*m**2 >> Iyy_gross=1.135# kg*m**2 >> Izz_gross=1.759# kg*m**2 >> Ixz_gross=0.1204# kg*m**2 >> #gross inertia matrix >> I_gross=Matrix([[Ixx_gross,0,-Ixz_gross], >> [0,Iyy_gross,0], >> [-Ixz_gross,0,Izz_gross]]) >> # current cg m and I using interplation based on fuel >> cg=(fuel/(m_gross-m_empty))*(cg_gross-cg_empty)+cg_empty >> m=m_empty+fuel >> m_dot=-Fuelflow >> I=(fuel/(m_gross-m_empty))*(I_gross-I_empty)+I_empty >> I_dot=m_dot*((I_gross-I_empty)/(m_gross-m_empty)) >> ########### >> rHub=Matrix([0,0,0]) >> #cg=Matrix([0.159,0,0.090]) >> cp=Matrix([0.1425,0,0]) >> #### cross product function >> def cross(a, b): >> c = [a[1]*b[2] - a[2]*b[1], >> a[2]*b[0] - a[0]*b[2], >> a[0]*b[1] - a[1]*b[0]] >> return c >> ######## total propulsion forces and moemnts #########3 >> Tx=F_prop >> Ty=0 >> Tz=0 >> M_Tx_temp=-M_eng >> M_Ty_temp=0 >> M_Tz_temp=0 >> >> #propulsion force caused moments based on the application point (usually >> the propeller hub) >> M_Tx_prop,M_Ty_prop,M_Tz_prop=Matrix(cross(Matrix([Tx,Ty,Tz]),(cg-rHub))) >> M_Tx=M_Tx_temp+M_Tx_prop >> M_Ty=M_Ty_temp+M_Ty_prop >> M_Tz=M_Tz_temp+M_Tz_prop >> ############ aerodynamics forces and moments ############ >> >> X_aero=CX*q_bar*S >> Y_aero=CY*q_bar*S >> Z_aero=CZ*q_bar*S >> L_temp=Cl*q_bar*S*b >> M_temp=Cm*q_bar*S*c >> N_temp=Cn*q_bar*S*b >> # since cross() return a list, it is required to transform to Matrix to >> perform the math opration >> >> L_aero,M_aero,N_aero=Matrix(cross(Matrix([X_aero,Y_aero,Z_aero]),(cg-cp)))+Matrix([L_temp,M_temp,N_temp]) >> ####### total aerodynamic and propulsion forces and moments #############3 >> X=X_aero+Tx >> Y=Y_aero+Ty >> Z=Z_aero+Tz >> L=L_aero+M_Tx >> M=M_aero+M_Ty >> N=N_aero+M_Tz >> >> #############equations of motion################ >> ## derived after the Simulink block : Custom Variable Mass 6DoF (Euler >> Angles) >> ## since Aerosonde model use this block >> Vb=Matrix([u,v,w]) >> p_q_r=Matrix([p,q,r]) >> #total forces matrix >> F=Matrix([X+m*gx,Y+m*gy,Z+m*gz])-Vb*m_dot >> # base on the equtions from Matlab help which is >> # Fb=m*(Vb_dot+cross(p_q_r,Vb))+m_dot*Vb >> # where Vb_dot=[u_dot,v_dot,w_dot] >> # then we can get u_dot,v_dot,w_dot as follows: >> u_dot,v_dot,w_dot=F/m+Matrix(cross(Vb,p_q_r)) >> # total moments matrix >> M=Matrix([L,M,N]) >> # base on the equtions from Matlab help which is >> # M=I*p_q_r_dot+cross(p_q_r,I*p_q_r)+I-dot*p_q_r >> # where p_q_r_dot=[p_dot,q_dot,r_dot] >> # then we can get p_dot,q_dot,r_dot as follows: >> p_dot,q_dot,r_dot=I.inv()*(M-Matrix(cross(p_q_r,I*p_q_r))-I_dot*p_q_r) >> >> # the kinematic equations >> >> x_I_dot=cos(theta)*cos(psi)*u+(-cos(phi)*sin(psi)+sin(phi)*sin(theta)*cos(psi))*v\ >> +(sin(phi)*sin(psi)+cos(phi)*sin(theta)*cos(psi))*w >> >> y_I_dot=cos(theta)*sin(psi)*u+(cos(phi)*cos(psi)+sin(phi)*sin(theta)*sin(psi))*v\ >> +(-sin(phi)*cos(psi)+cos(phi)*sin(theta)*sin(psi))*w >> z_I_dot=-sin(theta)*u+sin(phi)*cos(theta)*v+cos(phi)*cos(theta)*w >> phi_dot=p+(q*sin(phi)+r*cos(phi))*tan(theta) >> theta_dot=q*cos(phi)-r*sin(phi) >> psi_dot=(q*sin(phi)+r*cos(phi))*sec(theta) >> >> ############### trim for steady turn ############# >> ###steady flght constrians >> #u_dot=0,v_dot=0,w_dot=0,p_dot=0,q_dot=0,r_dot >> ### additional constrains >> #phi_dot, theta_dot is zero, psi_dot is turn rate >> #take psi_dot = 0.02 as an example >> u_dot_=u_dot.subs({deltFlap:0,dotAlpha:0,Ze:-1000,fuel:2}) >> v_dot_=v_dot.subs({deltFlap:0,dotAlpha:0,Ze:-1000,fuel:2}) >> w_dot_=w_dot.subs({deltFlap:0,dotAlpha:0,Ze:-1000,fuel:2}) >> p_dot_=p_dot.subs({deltFlap:0,dotAlpha:0,Ze:-1000,fuel:2}) >> q_dot_=q_dot.subs({deltFlap:0,dotAlpha:0,Ze:-1000,fuel:2}) >> r_dot_=r_dot.subs({deltFlap:0,dotAlpha:0,Ze:-1000,fuel:2}) >> phi_dot_=phi_dot >> theta_dot_=theta_dot >> psi_dot_=psi_dot >> Fuelflow_=Fuelflow.subs({deltFlap:0,dotAlpha:0,Ze:-1000,fuel:2}) >> >> MomentofInertiaofEngAndProp_=MomentofInertiaofEngAndProp.subs({deltFlap:0,dotAlpha:0,Ze:-1000,fuel:2}) >> >> #the relationshiop between p,q,r and eular angles are given as >> # p=-psi_dot*theta >> # q=psi_dot*sin(phi)*cos(theta) >> # r=psi_dot*cos(phi)*cos(theta) >> # which are expressed as >> p_equ=(p+psi_dot*theta) >> q_equ=(q-psi_dot*sin(phi)*cos(theta)) >> r_equ=(r-psi_dot*cos(phi)*cos(theta)) >> >> >> result_steadyturn=nsolve([u_dot_,v_dot_,w_dot_,p_dot_,q_dot_,r_dot_,phi_dot_,theta_dot_,psi_dot_-0.02, >> >> p_equ,q_equ,r_equ,Fuelflow_,MomentofInertiaofEngAndProp_], >> >> [u,v,w,p,q,r,phi,theta,psi,deltElevator,deltAileron,deltRudder,thr,omega], >> [10,3,0,0,0,0,0,0,0,0,0,0,0.5,500]) >> > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > Visit this group at http://groups.google.com/group/sympy?hl=en. > For more options, visit https://groups.google.com/groups/opt_out. > > -- You received this message because you are subscribed to the Google Groups "sympy" group. 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