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Okay. I guess it doesn't really matter in the end, since the partial derivatives \frac{\partial V}{\partial \theta_1} and \frac{\partial V}{\partial \theta_2} are identical for both equations, namely: \frac{\partial V}{\partial \theta_1}=(m_1+m_2) \sin\theta_1 g l_1 \frac{\partial V}{\partial...

Thank you. I think I see what you mean. Let me recalculate it.

Hello, everybody. This website and many others define the potential energy of a double pendulum as: V=-(m_1+m_2) g l_1 cos\theta_1-m_2 g l_2 cos\theta_2 However, I came up with the following equation: V= (m_1+m_2) g l_1 (1-cos\theta_1)+m_2 g l_2 (1-cos\theta_2) I started from the position...

Homework Statement How can one show/prove that for a beam (hinged supports on both ends) subjected to bending due to a uniformly distributed load over its entire length, the virtual work of internal forces is equal to the virtual work of external forces? Given are the length of the beam (L)...

I guess the possible inputs have to be: \bar{X}\bar{Y}\bar{Z} 000 \bar{X}\bar{Y}Z 001 \bar{X}YZ 011 \bar{X}Y\bar{Z} 010 XY\bar{Z} 110 XYZ 111 X\bar{Y}Z 101 X\bar{Y}\bar{Z} 100 Thank you. Can't I just assume 5 states then? A - all full B - get sand C - 1st full (entry action: refill) D...

Is it possible that all states always reduce to one, no matter if I assume 4 or 8? Either I'm doing something wrong here or I don't know why. Can anyone help? Thanks.

I know what you mean, but that is not the case here. We don't have "general" states representing the signals from all the sensors at a time, each of them is treated separately as a state. So state 1 - 1st is empty, state 2 - 2nd empty and so on.

Thanks, maybe I wasn't too precise, the bins don't have to be filled in one cycle. One cycle involves refilling only one bin which narrows the amount of possible states down to 4 I guess. After refilling, the arm returns to the initial state and so on. There would have to be 4 outputs...

Homework Statement Hi everyone; I've got a problem to solve that involves three containers which should be filled with sand, each of them has a sensor attached at the same level, so if the amount of sand drops below that limit, it will be refilled. If all were empty, the refilling arm...

Okay, I already figured it out...

Hi there; I guess this must be really easy and obvious but I just can't seem to be able to figure it out right now. I need to find (grapho-analytically) the acceleration of B (which is obviously the same as of C) in the position show in the picture. v_1=2 m/s is the input velocity...

Frankly, I've only seen lb for both force and mass used in books. It always seemed quite confusing to me.

Thanks for your reply, nvn. Actually I figured out where my teacher made a mistake. Obviously he didn't multiply 1.35Nm by 20 while converting the unit from ft*lb. 1{ft}\cdot{lb}\approx1.355817456Nm That said, if I assume the potential energy to be 27Nm, then my results are almost the same...

[solved] resulting velocity of 2 particles Homework Statement Homework Equations conservation of momentum m_Av_A'=m_Bv_B' v_A'=\frac{m_B}{m_A}v_B' conservation of energy...

Right, at the time I didn't realize that there should be six reactions at a fix support. Thanks.