Question: Error, (in Physics:-Vectors:-+) vectors projected over different basis

I posted a similar question about typesetting:-delayDotProduct. I used two different methods to solve the same vector calculus problem and came up with two seperate problems, though both are using the with(Physics[Vectors]) package. Below is my code showing the error.

Thanks for any help you all can give on this.

Cheers,

Dave
 

``

Problem 3-1

 

basis issue

 

restart; with(Physics[Vectors]): Setup(mathematicalnotation=true);
Coordinates(cartesian); Coordinates(X = [x,y,z,t])

[mathematicalnotation = true]

 

Coordinates(cartesian)

 

Coordinates(X = [x, y, z, t])

(1.1.1)

D1:=D1_(t,x,y,z);
B:=B_(t,x,y,z);
E:=E_(t,x,y,z);
j__p:=j__p_(t,x,y,z);

D1_(t, x, y, z)

 

B_(t, x, y, z)

 

E_(t, x, y, z)

 

j__p_(t, x, y, z)

(1.1.2)

f1:=epsilon=epsilon__0+rho/(B_.B_);

epsilon = epsilon__0+rho/Physics:-Vectors:-Norm(B_)^2

(1.1.3)

f2:=Nabla.D1=0;
f3:=Nabla.(epsilon*E)=0;

Physics:-Vectors:-Divergence(D1_(t, x, y, z)) = 0

 

epsilon*Physics:-Vectors:-Divergence(E_(t, x, y, z)) = 0

(1.1.4)

poisson equation and assume sigma is sigma__p

f4:=epsilon__0*(Nabla.E)=sigma__p(t);

epsilon__0*Physics:-Vectors:-Divergence(E_(t, x, y, z)) = sigma__p(t)

(1.1.5)

f5:=diff(sigma__p(t),t)+Nabla.j__p=0;
f6:=j__p=n*e(v__i_p-v__e_p);
f7:=j__p=n/(B_.B_)*(m__i+m__e)*diff(E,t);
f8:=j__p=rho/(B.B)*diff(E,t);

diff(sigma__p(t), t)+Physics:-Vectors:-Divergence(j__p_(t, x, y, z)) = 0

 

j__p_(t, x, y, z) = n*e(v__i_p-v__e_p)

 

j__p_(t, x, y, z) = n*(m__i+m__e)*(diff(E_(t, x, y, z), t))/Physics:-Vectors:-Norm(B_)^2

 

j__p_(t, x, y, z) = rho*(diff(E_(t, x, y, z), t))/Physics:-Vectors:-Norm(B_(t, x, y, z))^2

(1.1.6)

f9:=diff(f2,t);
f10:=diff(f3,t);
f11:=diff(f4,t);

Physics:-Vectors:-Divergence(diff(D1_(t, x, y, z), t)) = 0

 

epsilon*Physics:-Vectors:-Divergence(diff(E_(t, x, y, z), t)) = 0

 

epsilon__0*Physics:-Vectors:-Divergence(diff(E_(t, x, y, z), t)) = diff(sigma__p(t), t)

(1.1.7)

f12:=isolate(f11,diff(sigma__p(t),t));
f13:=subs(f12,f5);
f14:=subs(f8,f13);
f15:=isolate(f14,Nabla.diff(E_(t,x,y,z),t));

diff(sigma__p(t), t) = epsilon__0*Physics:-Vectors:-Divergence(diff(E_(t, x, y, z), t))

 

epsilon__0*Physics:-Vectors:-Divergence(diff(E_(t, x, y, z), t))+Physics:-Vectors:-Divergence(j__p_(t, x, y, z)) = 0

 

epsilon__0*Physics:-Vectors:-Divergence(diff(E_(t, x, y, z), t))+Physics:-Vectors:-Divergence(rho*(diff(E_(t, x, y, z), t))/Physics:-Vectors:-Norm(B_(t, x, y, z))^2) = 0

 

Error, (in Physics:-Vectors:-+) vectors projected over different basis

 

 

NULL


 

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