Stability Definition and 524 Threads

Hello, guys I am struggling with attaining stability values for u in solving the diffusion equation. The stability of u depends on the value of r from : D=1000; r0=1000; std=1.0; tau=1.0; IP=2500; %initial pressure % % Radial grid and inhomogeneous term nr=51; dr=r0/(nr-1)...

Homework Statement A particle of mass m moves under a central force ##\mathbf{F}(\mathbf{r}) = -\frac{\mu}{r^2} e^{-kr} \hat{r}##. The particle undergoes motion in a circle if ##h^2 = (a\mu/m)e^{-ka}##. I have shown that if ##u(\theta) = 1/r,## then the orbit eqn for ##u(\theta)## becomes...

i need show that at the following system the zero solution is nominally stable, using some change of variable that transforme in a linear system \frac{dx}{dt}=-x + \beta (x^2+ y^2) \frac{dy}{dt}=-2y + \gamma x y i tried with the eigenvalues of the Jacobian matrix at (0,0), but one of...

Hi everyone, one my textbook there is written (if two system blocks are asintotically stable and are in series, their product will be asintotically stable), but I've heard that sometimes the transfer function of the controller could be not asintotically stable in some cases (see p.i.p...

How do Zener diode keep voltage constant if input voltage is less than Zener voltage

A new article in Sciam discusses a possible fate of the unvierse: http://www.scientificamerican.com/article.cfm?id=how-the-higgs-boson-might-spell-doom-for-the-universe&page=2 I know there has been some discussion of this since the Higgs mass (and it looks more and mroe like a standard model...

HI Everyone. First of all, I'm not an aeronautical or mechanical engineer. I'm an electronics engineer but I'm currently doing a group project where I'm required to carry out a stability analysis on an aircraft that we've designed using the simulator software, X Plane. I apologise in...

Hello, I've designed a FLC controller for an UAV and I want to analyze its dynamic stability. In all "Flight dynamics and control" books I've read, the analysis is based on transfer functions of the aircraft (and exemplified on a specific aircraft like Cessna 172) and of the pilot (human or...

Hi I have been working through and want to plot the graph (fig1.2) on page 10 also found here http://www.amazon.com/dp/0198509545/?tag=pfamazon01-20 or here http://arxiv.org/pdf/hep-ph/0003170v1.pdf I have worked through and got the formula for the triviality bound and that is fine and got...

I have a very complicated stiff system, which can be expressed as: x^{\prime}(t)=A(x,y)-B(x,y) y^{\prime}(t)=C(x,y)-D(x,y) I decided to solve it with the fixed-point iteration method (http://en.wikipedia.org/wiki/Fixed_point_iteration) but I also have to use adaptive time stepping to...

Can someone please explain WHY is it when the poles of F(s) have negative real parts, the system is stable. Why is it when the poles of F(s) have positive real parts the system is unstable? Why is it when the real parts of the poles of F(s) equal to 0 the system becomes metastable...

Homework Statement I have not been doing Lyapunov for a while and when doing an ordinary Lyapunov problem the other day, I ran into a funny situation. The correct way of doing it: \begin{align} \dot{e} &= \frac{1}{L}(u - R(e + x_{ref})) \\ V(e) &= \frac{1}{2}Le^2 \\ \dot{V} &= Le\dot{e} = Le...

I'm having trouble understanding the relationship between a system's energy level and its stability (in a general sense). My understanding is that chemical and physical systems experience a driving force that pushes them toward the lowest possible energy state (ignoring quasi-steady states...

Homework Statement A (rectangular homogeneous) picture is hung with a nail on the wall from a twine. Neglecting the friction of the twine with the nail and that of the wall with the picture, a.-Could there exist equilibrium in other positions than the one where the picture is hanging...

I am confused by the concept of stability and condition. As I understand it, condition is defined by how much the output changes when the input changes. But why is it linked to the problem and not the algorithm? What if I have two algorithms that calculate the same thing but in a completely...

Suppose we have a dynamical system x_{t+1} = Ax_{t} where A is matrix, x is vector. We suppose that $x$ always grow as time goes on. If we treat equilibrium as the whole time evolution(path) of x given x_0 = a and no disturbance to the value of x - that is $x$ follows from the initial...

Homework Statement State the strongest stability property of the system (stable, asymptotically/exponentially): \begin{align} \dot{x_1} &= x_2 \\ \dot{x_2} &= -x_1 e^{x_1 x_2} \end{align} Homework Equations With the Lyapunov function candidate: \begin{equation} V(x) = \frac{1}{2}(x_1^2...

Homework Statement The trajectory of an arrow in space obeys the following system of equations: \dot{x} = y+(x^2+y^2-3)^2 (x^3-x+xy^2) \dot{y} = y+(x^2+y^2-3)^2 (y^3-y+x^2y) 1. Questions a) Derive an ODE for the radial coordiante r(t) = \sqrt[]{x^2(t)+y^2(t)} b) Show that the...

I have been thinking about numerical methods for ODEs, and the whole notion of stability confuses me. Take Euler's method for solving an ODE: U_n+1 = U_n + h.A.U_n where U_n = U_n( t ), A is the Jacobian and h is step size. Rearrange: U_n+1 = ( 1 + hA ).U_n This method is...

Decreasing Stability order of given I, II, III, IV (in order) A)IV>I>II>III B)I>IV>III>II C)I>II>IV>III D)IV>II>I>III (My Answer) Since the IV is most stable, only A and D answers are worth checking. They only differ by stability order of I and II. Then I checked by determining...

I am looking at this pretty chart: http://upload.wikimedia.org/wikipedia/commons/8/80/Isotopes_and_half-life.svg My question is, how sensitive is it to the variation of SM parameters? Imagine that I am sitting in front of some magic TV, where the image above is displayed. Below there are...

I have observed that when the outermost orbital is half filled (like Nitrogen 1s2 2s2 2p3), the atom has a higher stability (or a lower binding energy). Why is this so? I have heard it has to do with the fact that electron spin is maximized at that point but it still does not make sense to me...

Hi everyone. I'm kind of new here, please be nice. So I was reading up some physics and came across the fact that if the no. of neutrons is too high compared to the no. of protons, the nucleus becomes unstable. I can understand why this happens with protons, due to the coloumbic repulsion...

a system is said to be stable if its impulse response approaches zero for sufficiently large time. why? please give me an satisfying answer..

For this problem I have taken laplace(one-sided) transform of h(t) which gives me H(s)=1/(s-α). From this I can state that α must be -ve for G(s) to be stable. But my problem is while taking one-sided Laplace Transform the exp(βt)u(-t) part gives 0. So in H(s) according to my calculation, β...

Hello, I am looking for research results, report etc. dealing with -aerodynamic efficiency and static longitudinal stability- Couldn´t find anything useful yet! Any ideas would be very much appreciated. Best Regards, granby

I was assigned a multistep task by my professor so I first made the molecule with ChemDraw, then I ran an optimisation using B3LYP/6-31G. I then ran a frequency scan and checked for any imaginary frequencies. There were no negative frequencies and my understanding is that this means that...

If I place a bicycle wheel on the floor, it flips over and falls down... Same is with the toy top. But when the wheel or the top spin, they remain stable. Can someone please explain the physics behind this?

I've just started a course on organic chemistry and the professor said some things which did'nt exactly make sense to me: 1) In a period, atoms are more electronegative as we go to the right. The more electronegative an atom is, the more stable it becomes. 2) In a group, atoms increase...

We have to determine in which of the following options, the first ion is more stable than the second. 1. 2. 3. 4. 5. 6. Attempt at the question 1. Since in the first one, +ve charge is due to bonding, not deficiency of electrons. 2. First one can get lone pair from N. 3. N...

Homework Statement Two sticks 1 and 2 are attached together at the point B and the stick 1 is placed on point A and all these sticks can be rotated with no friction. If the stick 2 rotated freely around point B, in which direction the stick 2 will rotate? Homework Equations I°ω°=Iω...

I admit I am a bit out of practice when it comes to DiffEq. I think I am either forgetting a simple step or getting my methods mixed up. Homework Statement The problem concerns a pendulum defined by d2θ/dt2 + (c/mL)(dθ/dt) + (g/L)sinθ = 0 where m=1, L=1, c=0.5, and of course g=9.8 After...

x'=y-x^3 and y'=-x^5 I've worked the jacobian which is [-3x^2 1;-5x^4 0] and the equilibrium is at (0,0) so jac = [0 1;0 0] and eigenvalues are both 0 so is the stability non isolated point? and what i can say about the basin of attraction of the origin? Could anyone help me...

I have heard much about how careers in aerospace engineering and astrophysics can be hard to find, one has to move around a lot, and the salary is not great. As far as money goes I don't care too much, but I'd like to make at least 75k a year, but I don't want to have to move around more than 2...

Why do U and Th (and Pu) have so long half lives in comparison with the lighter elements following Bi (i.e. Po, Ra, Rn, Fr, At ..)?

Homework Statement Basically I found the following system of DE's: \frac{dx}{dt}=y \frac{dy}{dt}=-\frac{g}{l} \sin x - \frac{cy}{ml}. (Damped pendulum) I'm asked to analize the stability of the critical points x=0, y=0 and x=\pi, y=0. Using intuition the first point is asymptotically stable...

Hello all and thanks in advance for whatever help you might be able to offer. I am currently working on a project where I am trying to find the A matrix for longitudinal stability analysis, ultimately to get my short period and phugoid modes to determine my level of handling (for any of you...

Hello! I'm doing a modal analysis and I'm trying to extract modal parameters from my aqcuired data. I'm using the Pulse Reflex Software. I got to the point where the Software provides me with a MIF and a stability diagram and I am to choose the parameters. However, I am unsure how...

https://dl.dropbox.com/u/73421703/b1.jpg hi there , I'm asking for help with this one! I should solve that problam through energy method. Given single force Q(not shown in the picture) on the edge of the cantilever(the right-end of the beam), what I'm looking for - The critical P(axial force)...

Basically I'm tying to work on a project that requires a heavy battery mounted on top of a foam floater. i believe that as long as the centre of gravity of the battery and the centre of buoyancy of the foam is close to each other, they will be stable in water or while floating on water. Correct...

In my book, it's written that the phenyl cation can't be stabilized by resonance. I can't think of any reason why this is so. All the conditions for resonance are satisfied : all carbon atoms lie in one plane, all possible canonical structures will have the same number of unpaired electrons...

This is just a simple conceptual question. When we try to calculate a nuclear binding energy of some nucleus, we get the mass defect(del M) and find the binding energy by using (del M)c^2 right? Well, what I do not understand is this. For instance, let's take a formation of a...

Hi! This is a very general question. I am trying to get my head around the concept of mappings in relation to non-linear dynamical systems. I have that The autonomous vector field $$\dot{x} = f(x)$$, $$x \in \bf{R}^n$$ has a fixed point $f(\bar{x}) = 0 $ and DEFINITION (LIAPUNOV STABILITY)...

So I saw a video on youtube: http://youtu.be/uhS8K4gFu4s And so I thought I'd try to understand the whole stable orbit thing. So first you have a simple energy equation of E = K + U. K = (1/2)mv^2 (kinetic energy) U = -GMm/r^2 (gravitational energy) r = radius of orbit v = velocity of...

Homework Statement If we have a cuboid like this one *It won't let me upload the picture or include a link but if you Google cuboid its the first picture* We know that the mas moment of inertia through the centroid is different for each face. So the yellow has the greatest mass moment of...

I often hear that for planet to have life on it it must have proportionaly large moon to keep it's axial tilt small like Earth is between 21.5° to 24.5° and not like Mars that varies from 15° to 35° which makes destructive effect on possible life that could flourish. But doesn't Venus have...

Hi all Suppose for a dynamical system \dot x=f(x) , x \in \mathbb R^n there exists finite number of isolated equilibria, each of which is locally stable (i.e eigenvalues of the associated Jacobian have negative real parts). My question is: Can this happen for more than one equilibrium...

As we all know, the nuclear stability graph strays away from the y=x line from mass no. = 20 onwards. Why is that?

Hi i am not goin goin going to lie Fluid Mechanics is not my strongest subject. Im struggling to calculate the Metacentric height. Ive got the following: Total weight of assembly (W) = 2.447kgf Ajustible weight (w) = 0.204kgf Breadth of pontoon (L) = 360mm Height of metacentre...

Let's say I have the following transfer function: G(s)=\frac { s-1 }{ { s }^{ 4 }+2{ s }^{ 3 }+{ 3 }s^{ 2 }+{ 4s }+5 } Which is run through MATLAB to obtain the pole-zero format: G(s)=\frac { s-1 }{ ({ s }^{ 2 }+2.576s+2.394)({ s }^{ 2 }-0.5756s+2.088) } Using a quadratic solver...