Stability Definition and 478 Threads

Hi all, I would be greatful is someone could kindly enlighten me as to the correct interpretation of the appended bode plots. My understanding when interpreting bode plots is that we desire 0 gain where the phase is equal to or exceeds 180 degrees (marginally stable / unstable). In...

Homework Statement The transfer function of an LTI system H(s) = (s^2 + 2)/(s^3+2s^2+2s+1) Find the followings i) pole-zero pattern of H(s) ii) Stability of the system iii) Impulse response h(t) Homework Equations Zero for which H(s) = 0 & Pole is for which H(s) = ∞ The...

The enthalpies of creating a cyclohexene radical isomers are: ORTHO: 444 kJ/mol META: 361 kJ/mol PARA: 401 kJ/mol The meta-isomer is most stable (that is the reason for the formation of meta product in radical addition). Para/meta isomers energies seem obvious - both carbons...

Homework Statement Given G(s) = 1/[(s^2+s+4)(s+6)] and C(s) = k, find the limit of stability of k. Also, what is the range of k such that the settling time is between 10 and 20 seconds. Homework Equations Provided above The Attempt at a Solution I have attempted to set this...

Homework Statement I'm having to figure out if a system is asymptotically stable, stable, or unstable. I am given the system block diagram. However, each constant block is actually a matrix. Also, there is an integral block thrown in there... Homework Equations The Attempt at a Solution In a...

I know there are other things that fail about the rutherford atom but as the electron is accelerating and radiating away energy it would fall into the nucleus, my question is how much energy would the electron need to gain so that the classical atom could be stable a hydrogen atom for example

Hi all, I need a model of a pneumatic pressure regulator. The model should be as simplest as possible and use an optimization solver to identify the regulator parameters in order to fit the performance I find in the datasheet of a commercial pressure regulator. I have already done a model...

I have a general question about the solution to the Diffusion equation using the explicit finite difference method. Now, it is known the solution is stable when D*dt/dx^2 is less than 0.5, based on the choice of time and space steps. However, how does the choice of the time and space steps...

I remember reading something, long ago, to the effect that any attempt at creating a CTC would be doomed by energy from vacuum fluctuations piling up through it and leading to explosive behavior (I think the idea originated in work done by Misner and Taub in 1969?). Does anyone know what is...

I'm a new comer to study the hadron physics.Why light quarks are more stable than heavy quarks and which one is easy to study? why? Thank you

Homework Statement Example: x'=y-x^3 y'=-x-y^3 Homework Equations The Attempt at a Solution Linear system x'=y y'=-x Is stable because Det(P-\lambdaE)=\lambda2+1 \lambda1,2=+-i So if I am not mistaken,than Ishould use Lyapunov stability,because the linear system is stable and I can't say...

Hi, I'm working on an invention that eliminates liquid slosh in partially filled liquid containers and allows for center of gravity control. I'm wondering if there is a market for such an apparatus where elimination of all slosh is needed. I am aware of baffles, sponges, and diaphragms. A...

Disclaimer: I'm not a physicist I've never quite grasped interstellar gas clouds (i.e. the material for new stars) and how they work. If they were too sparse, then you'd expect them to just dissipate. If they were too dense, then you'd expect them to collapse spontaneously. But yet they seem...

A question I am doing hints that the solution (y,\dot{y}) = (0,0) of \ddot{y} - \frac{2}{t}\dot{y} + y = 0 is unstable. I believe (although I am not 100% sure) that is true however I am struggling to prove it. I can rewrite the equation as a system of equations in matrix form to get \dot{x} =...

hi, I'm measuring my laser pointing stability with a focusing lens and a CCD. Could you guys tell me what would the relationship be between the offset from focal point in CCD and the angle with which the beam exits the laser? CCD is in focus.

U = Th + alpha rays 92p 90p 146n 144n I have heard that if n/p ratio exceeds 1.56, the substance becomes radioactive. Now, for Uranium, n/p ratio is 1.59. It gives out alpha rays in order to gain stability and in turn forms Thorium. n/p...

I have always been under the impression that I totally understood the mechanics working behind the stability of a bicycle i.e. i) the gyroscopic effect of the spinning wheel ii) weight of cycle and rider and iii) the centrifugal force acting on the CG when the bicycle follows a curve path. If...

How can I plot the runge kutta 4 stability region? I know on the i axis the max is \(\pm 2\sqrt{2}\). The plot makes a heart type shape. I don't know how to plot it though but would like to.

This question was prompted by reflecting after reading the standard textbook explanation that "the greater acidity of RCOOH vs ROH is due to the greater stability of the delocalised RCOO- ion causing the position of equilibrium to be further to the right". The equilibria can be written as...

I took a CFD class last semester (had to leave school though due to personal garbage). I am making a come back this fall and as some extra credit I am trying to numerically solve the unsteady laminar flow equation in a pipe. The equation is \dot{U} + U'' + K = 0 where dots denote the time...

I've heard this expression in nuclear physics: the "island of stability." I know it has to do with the stability of a heavy transuranium atom (at least i think so), but what precisely does that expression mean? And what does it have to do with quantum mechanics? Why is this "island" there...

I'm in my last year of college as an undergraduate physics B.S. and have so far tried astronomy and materials science research internships and haven't liked either of them that much. I enjoy the theory behind astrophysics but don't enjoy programming all day. On the other hand, I like the...

Suppose we have a matrix A that has eigenvalues λ1, λ2, λ3,... Matrix B is a matrix that has "very small" matrix elements. Then we could expect that the eigenvalues of sum matrix A + B would be very close to the eigenvalues λi. But this is not the case. The eigenvalues of a matrix are not...

Minkowski space and deSitter space have been shown to be stable in GR under small perturbations. Perturbations do not intensify in higher frequency modes--these solutions don't go haywire and develop black holes all over the place. Piotr Bizon has shown that Anti-deSitter (AdS) space is not...

I am stuck with another one -- Assume that f(x) has the following graph: (for graph please see the attachment) Consider the (1-dimensional) ODE: X’ = f(x): (a) Find all the xed points, and study their stability. (b) Draw the phase portrait of the system, as well as the graphs of the...

Hi PF, I've been wondering why lattice structures form in metals and in salts. Why do fcc or bcc structures reduce the energy of a system so that regular lattices are favorable over those whose atoms are randomly placed? Thanks, Pillow

Stability, Helmholtz free energy mathematical relation "proof" Homework Statement I must show that \left ( \frac{\partial ^2 F}{\partial V ^2} \right ) _T=\frac{\frac{\partial ^2 U}{\partial S^2} \frac{\partial ^2 U}{\partial V ^2} - \left ( \frac{\partial ^2 U}{\partial S \partial V} \right...

About 6 years ago, I made a precipitate of Lead Iodide in water by mixing Potassium Iodide and Lead Nitrate. I have kept the precipitate in a test tube. Would anybody know how stable is the precipitate over time. The temperature has been mostly between 20 and 32 degrees depending on the...

It is often stated that quantum mechanics is able to explain the stability of atoms. I think most explanations are cheating b/c the compare apples and oranges. There are two reasons in classical theory which indicate that atoms should be unstable: A) there is no minimum for the orbit; the...

Hello everyone! This is my first post here, and I'm a recent graduate (within 1yr) of a BS in Mechanical Engineering. I have always been a car nut, and I'm interested in designing, or installing and tuning, a stability control system for my car. I recently purchased a 2012 Subaru...

Hello, I'm currently modeling the profile of a droplet (sessile drop, axisymmetric) in matlab. I've coded differential equations, applied the solver, and I get a reasonable result, except that it spirals continuously. The ODE's in question are: \frac{dx}{ds}=cos(\theta)...

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...

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...