Recent content by Eidos

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    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?
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    Proof: All Blind-Memoryless search strategies are equivalent

    Thanks very much ^^ Thats exactly what I was looking for.