# Question:Physics Package

## Question:Physics Package

I am trying to learn to use the Physics Package.

There is also a tensor package. Do this packages work together?

I tried some examples from a mechanics book:

For a stresstensor the stessvector on a plane defined by its normal should be calculated.

I made it in the following way:

restart:with(Physics[Vectors]):
sigma[i,j]:=Matrix([[ 54 , -27 , 9 ],
[ -27 , 18 , 0 ],
[ 9 , 0 , -36 ]]);
n:=1/3*<2,-2,1>;
t:=sigma[i,j].n;

But this only a matrix, vector multiplication.

restart:with(Physics[Vectors]):with(Physics):
Simplify(KroneckerDelta[i,j]*KroneckerDelta[j,k]);
Simplify(KroneckerDelta[i,j]*KroneckerDelta[j,i]);
Simplify(KroneckerDelta[mu,nu]*KroneckerDelta[nu,mu]);
Simplify(KroneckerDelta[i,j]*KroneckerDelta[j,k]*KroneckerDelta[k,i]);
Simplify(KroneckerDelta[mu,nu]*KroneckerDelta[nu,rho]*KroneckerDelta[rho,mu]);
Simplify(KroneckerDelta[i,j]*c[j,k]);
Simplify(KroneckerDelta[mu,nu]*c[nu,rho]);

Depending weather I use mu nu rho or i j k , the results are different.

Sometimes the sum convention is  used. Sometimes not.

I need an introduction, how to use th physics package. Are the more physics examples?

For example, how to calculate the stress inside a 3d-beam.

Or the stress inside a thick tube with loads inside and at the ends.

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