\lim_{z \to 0} \frac{sin z}{z(z+i)}
I applied L'Hopital and I got:
\lim_{z \to 0} \frac{cos z}{2z+i}=\frac{1}{i}
Wolphram Alpha's solution is -i. What am I doing wrong?
Okay, I think I got it.
Using the equation of the mayor circunference of center (0,2) and radius R=3 from Mohr's circle, we make σ=0. Then we isolate the shear stress.
(σ-2)2+(τ-0)2=32
τ=√5
Now that I have the modulus, I want to know the normal direction of the plane in which shear stress...
Given the stress tensor in a point, determine the zero normal stress plane.
...2 3 0
T= 3 2 0
...0 0 5
----------------------
Eigenvalues: σ1=σ2=5, σ3=-1
It must be simple, but I don't know how to determine the normal vector of that plane analytically.
I know σ=0.
t=Tn=σ+τ=τ
If normal stress...
I don't know why he uses cos(σ+ψ) and sin(σ+ψ) instead of cos(σ) and sin(σ) when the matrix of the second line is separated.
That would make cos(σ+ψ)=cos(σ). Is this true? I can't see that relation. Because there is no similarity between the triangles formed by the vector (x,y) and the vector...
I was trying to deduce the 2D Rotation Matrix and I got frustrated. So, I found this article: Ampliación del Sólido Rígido/ (in Spanish).
I don't understand the second line. How does he separate the matrix in two different parts?
Thanks for your time.
When you look at a cube drawn in a 2D surface, you can see a projection of the third dimension, but no the whole third dimension. When you look at a moving hypercube in the third dimension, you are seeing a projection of the fourth dimension.
Homework Statement
A particle of mass M is on the top of a vertical circle without initial velocity. It starts to fall clockwise.
Find the angle with respect to the origin, where the particle leaves the circle.
Homework Equations
v=ωXr
The Attempt at a Solution
I used two unitary...