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1、symsa1a2lxfai1=x^4-2*l*x^3+l^2*x^2fai2=2*x^5-5*l*x^4+4*l^2*x^3-l^3*x^2v=a1*fai1+a2*fai2d2fai1=diff(fai1,x,2)d2fai2=diff(fai2,x,2)A=int((a1*d2fai1+a2*d2fai2)^2,x,0,l)fai1=x^4-2*l*x^3+l^2*x^2fai2=2*x^5-5*l*x^4+4*l^2*x^3-l^3*x^2v=a1*fai1+a2*fai2d2v=diff(v,x,2)A=in
2、t((d2v)^2,x,0,l)x=1/3*lfai1=x^4-2*l*x^3+l^2*x^2fai2=2*x^5-5*l*x^4+4*l^2*x^3-l^3*x^2v=a1*fai1+a2*fai2%(1)%(2)x=1/3*lV(L/3)=-(4*a2*l^5)/243+(4*a1*l^4)/81V1^2=x=2/3*lV(2L/3)=(4*a2*l^5)/243+(4*a1*l^4)/81V2^2=求和B=m1v1^2+m2v2^2=1/3*m*l*((-(4*a2*l^5)/243+(4*a1*l^4)/81
3、)^2+((4*a2*l^5)/243+(4*a1*l^4)/81)^2)A=(4*a1^2*l^5)/5+(4*a2^2*l^7)/7B=(-(4*a2*l^5)/243+(4*a1*l^4)/81)^2+((4*a2*l^5)/243+(4*a1*l^4)/81)^2dA=diff(A,a1)dB=diff(B,a1)simplify(dB)%(3)x=1/4*lV(L/4)=-(9*a2*l^5)/512+(9*a1*l^4)/256V1^2=x=2/4*lV(2L/4)=(a1*l^4)/16V2^2=x=3
4、/4*lV(3L/4)=(9*a2*l^5)/512+(9*a1*l^4)/256V3^2=求和B=m1v1^2+m2v2^2=(-(9*a2*l^5)/512+(9*a1*l^4)/256)^2+((a1*l^4)/16)^2+((9*a2*l^5)/512+(9*a1*l^4)/256)^2simplify((-(9*a2*l^5)/512+(9*a1*l^4)/256)^2+((9*a2*l^5)/512+(9*a1*l^4)/256)^2+(a1^2*l^8)/256)A=(4*a1^2*l^5)/5+(4*
5、a2^2*l^7)/7B=(-(9*a2*l^5)/512+(9*a1*l^4)/256)^2+((9*a2*l^5)/512+(9*a1*l^4)/256)^2+(a1^2*l^8)/256dA=diff(A,a1)dB=diff(B,a1)simplify(dB)
