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Question: What is generating the R[0] term, and how do I remove it?

Question:What is generating the R[0] term, and how do I remove it?

srntmpsn 5 Maple 2021
syntax differential-equations euler-lagrange
July 21 2022
1


I'm using Maple 2021, and my Euler-Lagrange equation is coming out with a R[0] term that should not be there. I want to know what is causing this error and how I can fix it.

restartNULL

Lagrangian

 

Leq := (1/2)*R^2*[-cosh(rho1(tau)^2)*(diff(t(tau), tau))^2+(diff(rho1(tau), tau))^2+sinh(rho1(tau)^2)*(diff(theta1(tau), tau))^2]+(1/2)*R^2*[-cosh(rho2(tau)^2)*(diff(t(tau), tau))^2+(diff(rho2(tau), tau))^2+sinh(rho2(tau)^2)*(diff(theta2(tau), tau))^2]-(1/2)*k*rho1(tau)^2-(1/2)*k*rho2(tau)^2-(1/2*(tanh(rho2(tau)-rho1(tau))+1))*(rho2(tau)-rho1(tau))^2; L := subs({diff(rho1(tau), tau) = var4, diff(rho2(tau), tau) = var6, diff(t(tau), tau) = var2, diff(theta1(tau), tau) = var8, diff(theta2(tau), tau) = var10, rho1(tau) = var3, rho2(tau) = var5, t(tau) = var1, theta1(tau) = var7, theta2(tau) = var9}, Leq)

(1/2)*R^2*[-cosh(rho1(tau)^2)*(diff(t(tau), tau))^2+(diff(rho1(tau), tau))^2+sinh(rho1(tau)^2)*(diff(theta1(tau), tau))^2]+(1/2)*R^2*[-cosh(rho2(tau)^2)*(diff(t(tau), tau))^2+(diff(rho2(tau), tau))^2+sinh(rho2(tau)^2)*(diff(theta2(tau), tau))^2]-(1/2)*k*rho1(tau)^2-(1/2)*k*rho2(tau)^2-(1/2)*(-tanh(-rho2(tau)+rho1(tau))+1)*(rho2(tau)-rho1(tau))^2

 (1.1)

Time Equation

 

epr11 := diff(L, var2); epr12 := diff(L, var1); epr13 := subs({var1 = t(tau), var10 = diff(theta2(tau), tau), var2 = diff(t(tau), tau), var3 = rho1(tau), var4 = diff(rho1(tau), tau), var5 = rho2(tau), var6 = diff(rho2(tau), tau), var7 = theta1(tau), var8 = diff(theta1(tau), tau), var9 = theta2(tau)}, epr11); epr14 := subs({var1 = t(tau), var10 = diff(theta2(tau), tau), var2 = diff(t(tau), tau), var3 = rho1(tau), var4 = diff(rho1(tau), tau), var5 = rho2(tau), var6 = diff(rho2(tau), tau), var7 = theta1(tau), var8 = diff(theta1(tau), tau), var9 = theta2(tau)}, epr12); epr15 := diff(epr13, tau); teq := epr15-epr14 = 0

2*R*[0]+(1/2)*R^2*[-4*rho1(tau)*(diff(rho1(tau), tau))*sinh(rho1(tau)^2)*(diff(t(tau), tau))-2*cosh(rho1(tau)^2)*(diff(diff(t(tau), tau), tau))]+(1/2)*R^2*[-4*rho2(tau)*(diff(rho2(tau), tau))*sinh(rho2(tau)^2)*(diff(t(tau), tau))-2*cosh(rho2(tau)^2)*(diff(diff(t(tau), tau), tau))] = 0

 (2.1)

NULL


 

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