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  1. E

    Work done by a distributed force on a string

    I've attached the picture of how the force enters the system. I agree with your assertion that the limits should include changes in t only. How will this effect my change of variable then? That is when I take the total derivative of dy, how do I exclude y_x dx from the total derivative?
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    Work done by a distributed force on a string

    Hi All I'd like to know how I could calculate the work done by a distributed force on a string. Let's say the force at a point x at a time t is given by F(x,t). Now the instantaneous amplitude of the string is given by y(x,t), say I think that the work done by the force in...
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    Including Dissipation in Kinetic Energy of Lagrangian

    Hi all I've found a way to include dissipation in the kinetic energy of the lagrangian for simple systems and I want to know if its ok to do this. My understanding is that dissipation is typically included using the Rayleigh dissipation function which is seperate from the Lagrangian. The...
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    Controllability of state space equation

    Where did you get those equations, your system is not doing what you want it to do I agree. I've tried using state feedback to solve your problem, here is what I got: u=-Kx where x=[x_1 \, x_2]^{T} and K=[K_1 \, K_2] You then choose the eigenvalues of the closed loop system...
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    Uncontrollable States in State Space

    Hi Guys/Gals If you end up with a row of zeros in the controllability matrix for a linear state space system, does that row correspond with the state that is uncontrollable eg. Assuming a linear state space system with 5 states, a row of zeros in the 4th row of the controllability matrix...
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    Effect of Pole Zero Cancellation on Nyquist Plot/Stability Criterion

    Another point to remember is that in practice pole-zero cancellation is basically impossible. The reason is that there will always be some parameter uncertainty in your system. The danger I'm addressing here is the pole-zero cancellation of a RHP pole or a RHP zero. If you don't cancel the...
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    Lagrangian: Inverted telescoping pendulum (robot leg)

    My pleasure :smile: I've thought about some further refinements where you make the stray torque depend on the angle of the leg if you want to. \frac{d}{dt}\frac{\partial L}{\partial \dot{\theta}}-\frac{\partial L}{\partial \theta}=\tau_s(\theta) Good luck! Let us know how it goes ^^
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    Lagrangian: Inverted telescoping pendulum (robot leg)

    As an aside, the other leg (i.e. the one not being balanced on) will enter the model as a stray (constant) torque in the \theta co-ordinate, so you'll probably need to include it to model the dynamics correctly. Lastly, you are probably only interested in the dynamics in the \theta...
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    Lagrangian: Inverted telescoping pendulum (robot leg)

    Im assuming a point mass at the tip of an extendable rod, angle is zero when the rod is upright, the x direction is along the horizontal and y direction is along the vertical. Let the position vector be r(t)=[x,y] r(t)=[x(t)-l(t)sin\theta(t),\, l(t)cos\theta(t)] Therefore...
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    Lagrangian: Inverted telescoping pendulum (robot leg)

    If you want to add in friction you can model it using Reyleigh dissipation, basically the frictional terms appear as extra forces, so you get: \frac{d}{dt}\frac{\partial L}{\partial\dot{q}_{i}}-\frac{\partial L}{\partial q_{i}}=Q_{i}-D_{i}\dot{q_{i}} Here Q_i are the external applied...
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    Godel and Fuzzy Sets

    Hello all Does Godel's incompleteness theorem still hold true for fuzzy sets? My feeling is that it doesn't since the" [Broken]no longer applies. Is this reasoning correct?
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    A proposed Hamiltonian operator for Riemann Hypothesis

    Before the mudslinging contest ensues. Your operator missed the third zero (around 25), why do you think that is? The other values are fairly close though ^^ If your operator can get them exact, how do you find any other zeros in the RH plane/ prove that aren't any? Not bad for an...
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    Why is -1*-1=1

    I've got an idea, if it for elementary maths I'd imagine they know what a function is. So why not draw f(x) = x^2 and show that f(-1) = (-1)^2 = 1 graphically :biggrin:
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    A proposed Hamiltonian operator for Riemann Hypothesis

    Are those the imaginary parts of the first three non-trivial zeros of the Riemann Zeta function?
  15. E

    Proof: All Blind-Memoryless search strategies are equivalent

    Thanks very much ^^ Thats exactly what I was looking for.
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    Proof: All Blind-Memoryless search strategies are equivalent

    Hi All Is there a proof that all blind-memoryless search strategies are equivalent? By equivalent I mean that no blind-memoryless search strategy can outperform any other in terms of time to goal and domain coverage. It seems to me that this is intuitively true. How would I go about...
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    Angular momentum conservation principle

    If the tape recorder is rigidly attached to the spacecraft then you can anticipate that the spacecraft will rotate in the opposite direction, if the tape recorder is floating freely and not in direct contact with the space craft hull, then the space craft will remain at rest and the tape...
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    Mega-Hertz floating point ADC

    Max is 8000 rpm I need to measure angular position in the Mhertz range in order to resolve the angular velocity on the order of 5\times 10^{-3} rad/s . So far I cant see the reflective surface as unbalancing the reaction wheel, although I will admit that I have not even done an order of...
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    Mega-Hertz floating point ADC

    Awesome! Thanks for the links :) Shaft encoding was something that I was looking at but was worried about the extra moment of inertia that it would add to the spinning disc. I forgot to mention the application, the goal is to measure the rpm and angular acceleration of a reaction wheel for a...
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    Mega-Hertz floating point ADC

    Im using intensity modulation of a laser beam on a spinning disc. In Ascii art. _________________................... /____ DISC ^.........|.............^....................\ ...........|..............* ...........|..............* ...........|..............*...
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    Mega-Hertz floating point ADC

    Hello Everyone :) Do any of you know of a floating point Analogue to Digital converter that can handle mega-hertz sampling frequencies? I need a really precise angular acceleration transducer which I'll integrate digitally to get angular velocity. Im using an FPGA to do the integration...
  22. E

    Body wavelength

    The same is true for any elongated conductor ;) Im convinced this thread was concerning body-wavelength. The antenna interpretation is here simply for the sake of offering an alternative to the other proffered explanation. Enjoy \'''\(..^.....^...)/'''/
  23. E

    Body wavelength

    How is that not a sound basis in science? Your body acting as an antenna is an observable, measurable, repeatable fact. Granted my order of magnitude calculation is not 100% accurate since I was assuming a dipole geometry. If I am in the wrong then we need a volunteer to go stand within a...
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    Body wavelength

    Human beings are also a 'perfect' antenna for some frequencies of electromagnetic radiation. Now, everything that is conductive can act as an antenna, but it 'recieves' frequencies better than others. Basically if we were a thin piece of wire that is 1.5 m tall, 100Mhz is the frequency which...
  25. E

    Calculus of variations

    I always thought that the principle of extremal action could be used to cast any physical problem into D.E. form. What made me think that was that Noether's Theorem was such a fundamental result. Briefly it states that the reason there are conservations of energy, momentum, angular momentum...
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    Impulse Train vs Sampling Function

    The heaviside step function (u(t)) is 1 for t>0 and 0 elsewhere. The dirac delta function, by definition is the derivative of the heaviside unit step function. \delta(t) = \frac{d}{dt}u(t) . Hence,\delta(t) is undefined at t=0 (since u(t) changes instantaneously at t=0), and zero...
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    Lost at MIT probability

    Homework Statement You are lost in the campus of MIT, where the population is entirely composed of brilliant students and absent-minded professors. The students comprise two-thirds of the population, and any one student gives a correct answer to a request for directions with probability...
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    ASCII from COM port to be used as 'keyboard' inputs

    Hey thanks alot! :smile: Keyinjector did the trick, we've got it working now.
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    Big bang?

    Jah, the" [Broken] project for which those guys won the nobel prize in 2007 was substantial evidence that the Big Bang happened :smile:
  30. E

    Condition for a 2nd order differential eqn to have bounded solutions?

    Would the Bilateral Laplace transform not help us here? (edit) Obviously if we restrict our domain to \mathbb{R}^{+} then the single sided Laplace transform can tell us when the function is bounded with x. I've found a link on something called Nachbin's Theorem...