I just saw the stickied thread about posting homework-type questions here... I hope this doesn't qualify as a homework-type question. Although it does involve debugging my thought process, it is also a conceptual question about why my reasoning is wrong. If this counts as a homework-type...
Referring to slides 3-4 (page 2) of this link: https://www.princeton.edu/~stengel/MAE331Lecture9.pdf
The author states the relationship between body rates [p q r] and Euler angle rates [φ_dot θ_dot ψ_dot]. I want to verify this but have been failing miserably...
My reasoning:
1) p, q, and r...
An aside: if angular momentum can be derived from linear momentum, then for example in 2D statics why can we get three independent equations using force balance in 2 directions and moment balance?
I was thinking of a couple basic mechanics problems lately. What if you have a rod sitting in space at rest, and you shoot a bullet at its center. Linear momentum is conserved, and the problem is quite trivial.
Now what if the bullet hit the rod slightly off of the rod's CG? I think linear...
I see, thank you for clarifying. Your explanation helps me see where these equations come from. So if I understand correctly, the moment equation, shear equation, and EI(x)\frac{∂^4w}{∂x^4}=-μ\frac{∂^2w}{∂t^2}+... are all basically just different derivatives of the same equation?
Indeed, I...
Sorry, I am still confused. So which equation is the actual Euler-Bernoulli beam equation?
So this:EI(x)\frac{∂^4w}{∂x^4}=-μ\frac{∂^2w}{∂t^2}+Fδ(x-L) is derived from this:
M=EI\frac{∂^2w}{∂x^2}
Did I understand correctly?
Or is EI(x)\frac{∂^4w}{∂x^4}=-μ\frac{∂^2w}{∂t^2}+Fδ(x-L) the...
OK, so it looks like I can integrate the Euler-Bernoulli equation twice to get moment?
EI(x)\frac{∂^4w}{∂x^4}=-μ\frac{∂^2w}{∂t^2}+Fδ(x-L)
Integrate once (using integration by parts, I guess):
EI(x)\frac{∂^3w}{∂x^3}-∫\frac{∂^3w}{∂x^3}(\frac{∂}{∂x}EI(x))dx = -μ\frac{∂^2}{∂t^2}(∫wdx) +...
M=EI\frac{∂^2w}{∂x^2}
1. What exactly is this? Is it like a geometric constraint? This equation doesn't seem to depend explicitly on external loading or beam boundary conditions.
2. Can I derive this starting from the Euler-Bernoulli beam equation?
I am dealing with a beam with...
Suppose we have a second-order system with the following transfer function:
G(s)= \frac{1}{s^{2} + 2ζω_{n}s +ω_{n}^{2}}
To figure out its resonant frequency, obtain its frequency response function and then maximize it with respect to ω. You get:
ω_{peak} = ω_{n}\sqrt{1-2ζ^{2}}
So it appears...
Thanks for your response.
I suppose if I thought of P as "mg" (except at the tip, and not the center of mass of the bar), then potential energy would become:
V= 1/2 K\dot{θ}2 + PLcos(θ)
which would indeed get me the correct answer.
I guess it's not clear to me why exactly you can...
Homework Statement
I am having trouble understanding how to apply Lagrange's equation. I will present a simplified version of one of my homework problems.
Imagine an inverted pendulum, consisting of a bar attached at a hinge at point A. At point A is a torsional spring with spring...
Hmm, I currently do not have access to any books, so an electronic resource would be preferable. But I will make sure to take a look at that book as soon as I get access to a library. Looks like it has some useful information.
I am looking for error propagation. I would like to determine a fit...
I am doing a calculation involving taking three or more temperature measurements and then plotting them against another quantity (dependent). I get a relationship that is pretty linear, so I take the line of best fit to obtain an equation with a slope and an intercept.
Now, my question is...
I'm collecting voltage data, and I need a resolution of at least .05mV, which I think I can provide over the range of voltages with my inexpensive A/D board. The problem is, the signal fluctuates maybe 1mV up and down, and so I get a noisy signal. I've tried running a low-pass filter through it...