EugeneKalentev

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These are answers submitted by EugeneKalentev

Hi mskalsi.

Add to the end of title "\n". 

For example, for 3 intervals: title = "Radial velocity curve of Polytropic Model of Index N=3\n\n\n"


Download 1.mw

The only thing that came up with this expression to divide into smaller and inserted into Mathtype in parts.


restart

NULL

Suppose we have some stress tensor

 

ST := Matrix(3, 3, {(1, 1) = -2.01*100000000, (1, 2) = -7.00*10000000, (1, 3) = -2.44*100000000, (2, 1) = -7.00*10000000, (2, 2) = 9.55*1000000, (2, 3) = -6.71*10000000, (3, 1) = -2.44*100000000, (3, 2) = -6.71*10000000, (3, 3) = -2.45*100000000})

ST := Matrix(3, 3, {(1, 1) = -2.01*100000000, (1, 2) = -7.00*10000000, (1, 3) = -2.44*100000000, (2, 1) = -7.00*10000000, (2, 2) = 9.55*1000000, (2, 3) = -6.71*10000000, (3, 1) = -2.44*100000000, (3, 2) = -6.71*10000000, (3, 3) = -2.45*100000000})

(1)

Transform it to the principal stresses (located on the main diagonal)

 

PST := Re(LinearAlgebra[MatrixInverse](LinearAlgebra[Eigenvectors](ST)[2])).ST.Re(LinearAlgebra[Eigenvectors](ST)[2])

PST := Matrix(3, 3, {(1, 1) = -486851343.56201524, (1, 2) = 0.14274120330810547e-1, (1, 3) = -.13130077719688416, (2, 1) = .18266209587454796, (2, 2) = 18142199.728485364, (2, 3) = 0.9578510047867894e-1, (3, 1) = -.5092253526672721, (3, 2) = 0.843829894438386e-1, (3, 3) = 32259143.83352987}, datatype = float[8])

(2)

Then you can get the equivalent (von Mises) stress

 

`σi` := sqrt(((PST[1, 1]-PST[2, 2])^2+(PST[2, 2]-PST[3, 3])^2+(PST[3, 3]-PST[1, 1])^2)*(1/2))

HFloat(5.1219794269403315e8)

(3)

NULL

 

``


Download Equivalent_stress_(von_Mises).mw

 

Fixed small bug


with(PDEtools):

PDE := (diff(f(x[1], x[2], p[1], p[2]), x[1]))*p[1]/m-(diff(f(x[1], x[2], p[1], p[2]), p[1]))*(2*k*x[1]-k*x[2])+(diff(f(x[1], x[2], p[1], p[2]), x[2]))*p__2/m-(diff(f(x[1], x[2], p[1], p[2]), p[2]))*(-k*x[1]+2*k*x[2]);

(diff(f(x[1], x[2], p[1], p[2]), x[1]))*p[1]/m-(diff(f(x[1], x[2], p[1], p[2]), p[1]))*(2*k*x[1]-k*x[2])+(diff(f(x[1], x[2], p[1], p[2]), x[2]))*p__2/m-(diff(f(x[1], x[2], p[1], p[2]), p[2]))*(-k*x[1]+2*k*x[2])

(1)

pdsolve(PDE)

PDESolStruc(f(x[1], x[2], p[1], p[2]) = _F4(p[2])+_F5(x[1], x[2], p[1]), [{2*(diff(_F5(x[1], x[2], p[1]), p[1]))*k*m*x[1]-(diff(_F5(x[1], x[2], p[1]), p[1]))*k*m*x[2]-k*_c[4]*x[1]*m+2*k*_c[4]*x[2]*m-(diff(_F5(x[1], x[2], p[1]), x[1]))*p[1]-(diff(_F5(x[1], x[2], p[1]), x[2]))*p__2 = 0, diff(_F4(p[2]), p[2]) = _c[4]}])

(2)

``


Download 7.mw


restart

-2 <= A/x and A/x <= 0

-2 <= A/x and A/x <= 0

(1)

`assuming`([solve(-2 <= 3/x and 3/x <= 0, x)], [x < 0])

RealRange(-infinity, -3/2)

(2)

``

``


Download 1.mw

Hello Dmitry Lyakhov.

Try to see the Physics package. The current version is available here

 

Best regards,

Eugene Kalentev

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