sorry , the previous reply is not for this question
On Friday, 18 January 2013 20:30:07 UTC, Renxian wrote:
> why would the code bellow yield this error?????? thanks
>
> 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')
>
> ####################################
> #g=var('g')
> g=9.81#m/s**2
>
> 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
>
>
> #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=0.0434
> 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
>
> ################ISA for Troposhere #############
> 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
> h=1000
> 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
> ####################################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/ua)
> Mach=Va/speedofsound
> q_bar=rho*Va**2/2
>
> #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*Abs(deltFlap)+CD_deltElevator*Abs(deltElevator)+CD_deltAileron*Abs(deltAileron)+CD_deltRudder*Abs(deltRudder)+CD_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*Matrix(3,1,[-CD,CY_w,-CL])
>
>
> ##############Fixed-pitch propeller##############333
>
> #Jar,CT,CP=var('Jar,CT,CP')
> omega=var('omega')
> #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###################
> thr=var('thr')
> 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-1.843*MAP**2+3.257/10**10*RPM**3+1.377/10**7*RPM**2*MAP+0.00003562*RPM*MAP**2+0.006149*MAP**3
>
> 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_P=432.4-0.3574*RPM-4.54*MAP+0.000005236*RPM**2+0.004861*RPM*MAP
> #Fuelflow,Power_P=var('Fuelflow,Power_P')
> #Power_P=var('Power_P')
> 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)
> #omega=integrate(MomentofInertiaofEngAndProp,omega)
> #omega2=integrate(MomentofInertiaofEngAndProp,omega)
> #without consider the moment caused by proleller force
> Tx=F_prop
> Ty=0
> Tz=0
> M_Tx=-M_eng
> M_Ty=0
> M_Tz=0
> #############equations of motion################
> #Ixx,Iyy,Izz,Ixz=var('Ixx,Iyy,Izz,Ixz')
> #gross moment of inertia
> Ixx=0.8244# kg*m**2
> Iyy=1.135# kg*m**2
> Izz=1.759# kg*m**2
> Ixz=0.1204# kg*m**2
>
> X=CX*q_bar*S+Tx
> Y=CY*q_bar*S+Ty
> Z=CZ*q_bar*S+Tz
> L=Cl*q_bar*S*b+M_Tx
> M=Cm*q_bar*S*c+M_Ty
> N=Cn*q_bar*S*b+M_Tz
>
> u_dot=X/m+gx+r*v-q*w
> v_dot=Y/m+gy-r*u+p*w
> w_dot=Z/m+gz+q*u-p*v
>
> p_dot=(Izz*L+Ixz*N-(Ixz*(Iyy-Ixx-Izz)*p+(Ixx**2+Izz*(Izz-Iyy))*r)*q)/(Ixx*Izz-Izz**2)
> q_dot=(M-(Ixx-Izz)*p*r-Ixz*(p**2-r**2))/Iyy
>
> r_dot=(Ixz*L+Ixx*N+(Ixz*(Iyy-Ixx-Izz)*r+(Ixz**2+Ixx*(Ixx-Iyy)*p)*q))/(Ixx*Izz-Ixz**2)
>
> 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 straight and level flight ############
> ###the aircraft is trimmed at
> Va25=Va-25
> #deltFlap=0
> #deltAlpha=0
> #straight level fight means
> #phi=0
> #p=0
> #r=0
>
> ###Initial seed value for solver
> #q=0
> #deltElevator=0
> #deltAileron=0
> #deltRudder=0
> #thr=0.5
> #u=25
> #v=0
> #w=0
> #omega=5236
> #theta=0
> #psi=0
> ###solve
>
> u_dot_=u_dot.subs({deltElevator:0,deltAileron:0,deltRudder:0,deltFlap:0,dotAlpha:0,omega:545.4,thr:0.07063})
>
> v_dot_=v_dot.subs({deltElevator:0,deltAileron:0,deltRudder:0,deltFlap:0,dotAlpha:0,omega:545.4,thr:0.07063})
>
> w_dot_=w_dot.subs({deltElevator:0,deltAileron:0,deltRudder:0,deltFlap:0,dotAlpha:0,omega:545.4,thr:0.07063})
>
> p_dot_=p_dot.subs({deltElevator:0,deltAileron:0,deltRudder:0,deltFlap:0,dotAlpha:0,omega:545.4,thr:0.07063})
>
> q_dot_=q_dot.subs({deltElevator:0,deltAileron:0,deltRudder:0,deltFlap:0,dotAlpha:0,omega:545.4,thr:0.07063})
>
> r_dot_=r_dot.subs({deltElevator:0,deltAileron:0,deltRudder:0,deltFlap:0,dotAlpha:0,omega:545.4,thr:0.07063})
>
> phi_dot_=phi_dot.subs({deltElevator:0,deltAileron:0,deltRudder:0,deltFlap:0,dotAlpha:0,omega:545.4,thr:0.07063})
>
> theta_dot_=theta_dot.subs({deltElevator:0,deltAileron:0,deltRudder:0,deltFlap:0,dotAlpha:0,omega:545.4,thr:0.07063})
>
> psi_dot_=psi_dot.subs({deltElevator:0,deltAileron:0,deltRudder:0,deltFlap:0,dotAlpha:0,omega:545.4,thr:0.07063})
> #omega_=omega.subs([p,r,phi,deltFlap,deltAlpha],[0,0,0,0,0])
>
>
> #result=nsolve([Va25,u_dot,v_dot,w_dot,p_dot,q_dot,r_dot,phi_dot,theta_dot,psi_dot,omega],
> #
> [q,deltElevator,deltAileron,deltRudder,thr,u,v,w,omega,theta,psi],
> # [0,0,0,0,0.5,25,0,0,5236,0,0])
>
> #result=nsolve([u_dot_,v_dot_,w_dot_,p_dot_,q_dot_,r_dot_,phi_dot_,theta_dot_,psi_dot_],
> # [q,deltElevator,deltAileron,deltRudder,u,v,w,theta,psi],
> #
> [0.000,0.0000,0.00000,0.0000,25.0,0.0000,0.00000,0.00000,0.00000])
>
> result=nsolve([u_dot_,v_dot_,w_dot_,p_dot_,q_dot_,r_dot_,phi_dot_,theta_dot_,psi_dot_],
> [q,r,p,phi,u,v,w,theta,psi],
>
> [0.000,0.0000,0.00000,0.0000,2.0,0.0000,0.00000,0.00000,0.00000])
>
>
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