(hint, you can debug nsolve() by adding verbose=True) It looks like the issue is that sec doesn't have the derivative defined.
Unfortunately, I tried defining it, but I then got ZeroDivisionError: matrix is numerically singular So there may be some more work for you to do. Aaron Meurer On Fri, Jan 18, 2013 at 1:30 PM, Renxian <[email protected]> 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]) > > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To view this discussion on the web visit > https://groups.google.com/d/msg/sympy/-/IEdPzm9B8dYJ. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > 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