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?
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...
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...
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...
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...
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...
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 ^^
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...
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...
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...
Hello all
Does Godel's incompleteness theorem still hold true for fuzzy sets?
My feeling is that it doesn't since the http://en.wikipedia.org/wiki/Law_of_excluded_middle" [Broken]no longer applies.
Is this reasoning correct?
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...
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: