5
votes
Limits of Euler-Bernoulli Beam Theory for Wide Plate in Flexure?
For a rectangular simply supported plate with length $a$ and width $b$ (Roark's Formulas for stress and strain):
$$\sigma_{max} = \sigma_b= \frac{\beta qb^2} {t^2} $$
$\beta$ ranges from 0.287 for a=...
- 22.8k
1
vote
Euler's formula with different coefficients and constants
For your example: 4cos(x) + 3isin(x) = ?
Plot a point at (4,3), find the distance from origin to point = $(x^2 + y^2)^½$
Then $4*cos(x) + 3*isin(x) = 5e^{i\theta}$
$\theta$ is the angle from the x ...
- 201
1
vote
Accepted
Euler's formula with different coefficients and constants
$$sin(\omega t) = Im\{e^{j\omega t}\} $$
But also
$$cos(\omega t) = Im\{je^{j\omega t}\} $$
Since
$$ j\left(cos(\omega t) + jsin(\omega t)\right) = jcos(\omega t) - sin(\omega t) $$
So then you can do:...
- 148
1
vote
How to plot quaternion constraint equation vs time
What equations do I need to find quaternions as a function of time? I have angular velocity
This reference page 14 and page 16 give the equation describing the derivative of the quaternion in terms ...
- 1,237
1
vote
Confusion regarding Euler rotations and Gimbal Lock
"Thus, the aircraft should be able to yaw appropriately (give rudder control surfaces and thrust)."
The above statement is correct for an aircraft freely flying in the air. In fact, for ...
- 1,237
1
vote
Does pressure in a centrifugal compressor increase along the path of the flow?
The more complex the geometry, the less likely generalized equations are going to be able to represent it. I understand what you are saying about the area of the volute getting larger as the fluid ...
- 8,285
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