Stability Definition and 525 Threads

Homework Statement [/B] Show that every trajectory, except r = 0, is asymptotically orbitally stable Homework Equations [/B] I have a hint that: I should think of two initially close trajectories (say a(0) = |x(0) - y(0)| sufficiently small and see how the difference evolves over time (the...

Homework Statement Find the range of K for the closed loop system to be stable. ##G_{OL}(s) = \frac{10}{s-5}## Homework EquationsThe Attempt at a Solution ##G_{CL}(s) = \frac{KGol}{1+Gol}## ##G_{CL}(s) = \frac{10K}{s-5+10K}## ##-5+10K>0## ##K>\frac{1}{2}## is this correct?

Hi everyone, I have created a simulation of the major bodies in the Solar System, using the exact positions, velocities, and masses etc. at midnight on Jan 10 (as provided by the NASA HORIZONS project). Using Newtonian gravity I numerically simulate the forces between all the bodies (with a...

Among the following species, which one does not exhibit resonance? 1. CH2=CH-CΘH2 (the 3rd carbon has a -ve charge) 2. CH2=CHCl 3. 1,4-Cyclohexadiene 4. CH3-NO2 Please, can anyone tell me which one and how did you get it?

Hola, I tried to give a proof of this theorem and then check it against the one given by my book(Fasano, Marmi - Analytical Mechanics); I feel like mine seems reasonable and pretty intuitive, but the one on the book is a bit different and I don't really understand it completely, so I'd like to...

I've written a space colony simulation game called High Frontier. It correctly simulates rotational stability when most of the mass is dominated by a single large spinning part. For example, a squat cylinder will be stable, but a long cylinder will end up tumbling end over end, as shown...

From my general understanding of physics we detect the creation of elements above 92 protons by the decay of the larger element into lighter elements. Since we use particle accelerators to create these heavier elements if we did create a completely stable isotope of element 118 for example...

I haven't done any Bode plots before, and so I'm reading about LDO stability and I came across this file, which I am trying to understand: http://www.ti.com/lit/an/slyt194/slyt194.pdf Under the stability analysis, it names the poles and zeroes. How are these calculated? I assume that the...

Are there equations that detail the stability of nuclei against beta decay? On a related point, I'm familiar with the chart that shows all the isotopes and their half-lives (with a good chunk undergoing beta decay), but I was wondering if that can be derived from first principles, just using the...

I'm currently studying the sensitivity of polynomial roots as a function of coefficient errors. Essentially, small coefficient errors of high order polynomials can lead to dramatic errors in root locations. Referring to the Wilkinson polynomial wikipedia page right...

Based on this link, in particular Figure 1, what is the exact meaning of the plot? To my understanding, it implies that for a given differential equation: $$ \frac {dy}{dt} = \lambda y $$ that the value ##\lambda \Delta t## has to be within the complex region shown in Figure 1 corresponding...

A one-dimensional dynamical system is given by $x′ = f(x), t \in [0,+\infty)$, where $f : \mathbb{R} \to \mathbb{R}$ is the smooth function defined as follows: $$f(x) = \begin{cases} x^4 \sin \left(\frac{1}{x}\right) & x \neq 0\\ 0 & x = 0. \end{cases}.$$ Find all the equilibrium points and...

I am reading about the stability of different numerical methods, although never exactly came across a good definition of what stability regions are. For example, considering this plot, what exactly is the figure representing? What do the unlabelled axes mean in this context? Are these stability...

I am embarrassed to ask this. I just want to make triple sure about this stability condition. In the attached plot, I have the open loop gain and phase plot in light green and closed loop gain and phase plot in dark blue. You can see the closed loop gain is 30dB which is about 22 or so. I want...

if there were no higgs field, would the second and third generation of fermions, such as the top quark, be exactly the same mass as first generation? is the coupling between the top quark and the higgs field the sole reason the top quark is heaviest SM particle? is there a reason the top...

Hello everyone, I need to know the stability and storage conditions of some solutions that I need to prepare. Is there a place where I can find this information (at least for most common solutions)? Or is there any bibliography to consult? Thanks

Hi, I have quite a superficial understanding of Droop control: http://www.openelectrical.org/wiki/index.php?title=Droop_Control https://en.wikipedia.org/wiki/Droop_speed_control I'm not after a super technically detailed explanation, but if anyone has any more detailed sources for how it is...

All of the planets should have individual orbits, and should be between the mass of Mercury and Mars. What can their orbits be in AU's? Is there a way to find out how close they can be without destabilizing each other? If we assume the star is about the same size as Sol.

Homework Statement from the equation r = n+3 , some notes stated n = number of hinges , while some book stated n as number of joints ...Which is true ? Homework EquationsThe Attempt at a Solution taking the example 3.1 , if it's number of joints , then there are 1 hinge (pin) , right ? I don't...

From what I understand, there are some industries in Mechanical Engineering that are typically boom/bust (like oil and gas and aerospace). I wonder which ones are the most stable? I think HVAC is a possibility, but I don't know if it's the kind of thing that I would like to work on for my entire...

I want to build a Self Balancing autonomous bicycle for which I need to know about CMG System,Can Any one please guide me to the basics of Gyroscope and CMG- Ebooks would be a great starts.

I know that, i studied it, but i can't actually make a picture in my mind, i can't really figure out why, i mean the forces and the torques are the same no? What's the big deal? What am i missing?

Does anyone know if there's any q-switching technique that makes use of an unstable resonant cavity (or some kind of switching of the cavity between stable and unstable) to achieve the pulse output?

Homework Statement Hi, can someone explain how they get this stability function. Homework Equations http://blob:http://imgur.com/840ee1fe-f09c-49ab-bdbb-7f953777f900 The Attempt at a Solution I have attempted to do it two ways, and I'm not sure if I'm just having an awfully bad day at maths...

What is the reason that aromatic compounds are more stable than other cyclic compounds ? Please provide answer in reference to MOT theory . Why are anti aromatic compounds so unstable ?

[This thread was split from https://www.physicsforums.com/threads/a-light-wave-and-a-sound-wave-travelling-together.878450/#post-5518001 as it's an interesting topic in its own right] That's actually an important point, in the core of neutron stars, the speed of sound increases with the...

What is the effect of on-grid PV systems, in terms of quality, voltage and stability? I'm not really sure how to answer this. Stability -- If consumer is tied to a PV power plant, grid stability could potentially be an issue. However, generally speaking, on-grid systems use the grid like a...

I'm doing some work on solar and I'm reading about properties of lamination materials, particularly EVA lamination. Anyway, one of it's properties is 'temperature stability' but I can't find a clear definition of what this means. EVA lamination is sandwiched in between a solar cell, so I can...

Hello everyone, If a nucleus consisting solely of mesons has enough mesons in it, will it be stable? Mesons are bosons, therefore (unlike baryons) they aren't effected by the pauli exclusion principle, so they all can acquire the lowest energy state. In theory, if there are enough mesons, the...

The condition for a stable orbit is given by (3.42), where ##V'## is the fictitious potential energy (potential energy of the corresponding fictitious one-dimensional problem) and ##r_0## is the radius of the circular orbit. The result ##n>-3## is obtained by using the convention that positive...

Homework Statement is it necessary to find the meta center for this question ? the formula of meta center is I /Vd , the I ( moemtn of inertia ) for rectangle is (ab^3) / 12 , but what is a ? what is b ? I'm confused now Homework EquationsThe Attempt at a Solution ρ[/B] gVsubmerged =...

Homework Statement Is sky wave signal less stable than ground wave signal? Homework Equations None The Attempt at a Solution Ground waves face attenuation because when it glides over the surface of earth, there will be induced fields which can oppose the wave. In case of sky waves, it...

Dear all, Consider the connection of two electrical circuits. Both circuits, Z1 and Z2, are stable and only one of them is non-passive. I.e., the eigenvalues are located in the LHP but Re{Z2(jw)}<0 in a frequency range. For studying the closed-loop stability, you represent the linear system by...

Homework Statement Homework EquationsThe Attempt at a Solution option 1: 1 degree C option 2: 1 degree C option 3: 3 degree C option 4: 1 degree C SO the answer should be option 3?

Homework Statement Homework EquationsThe Attempt at a Solution Shouldn't the answer be 4? It certainly isn't 1 or 3 because they have maximum -I effect

Homework Statement Homework EquationsThe Attempt at a Solution Shouldn't the answer be option 3 because the carbon there is a 3 degree carbon and it has the maximum number of alkyl groups attached to it?

Wald, General Relativity, p. 411, says that Minkowski space is unstable in semiclassical gravity. He gives a reference to this paper: Horowitz, "Semiclassical relativity: The weak-field limit," Phys. Rev. D 21, 1445, http://journals.aps.org/prd/abstract/10.1103/PhysRevD.21.1445 The Horowitz...

The top and Higgs mass determination arose the old discussion about electroweak vacuum metastablity. There is an interesting fact that with available data the universe places in the edge of stable and meta-stable zone tends to be inside the meta-stable region. This conclusion confirms up to...

Hello Physics Forum patrons! I am currently in search for some software and maybe hardware to analyze and map vibration/stability for rotating cutting tools (CNC milling). Being primarily a machine programmer and product designer, I have a very minimal understanding of vibration from a physics...

Every accelerated charge particle lose its engrgy in the form of electromagnetic wave but electron of an atom moving on stationary orbit do not emit any radiation. why? And why do accelerated charge particle lose energy in the form of electromagnetic radiation? Is there any relation between...

Homework Statement : [/B] In the image above, the toy consists of two identical mass hanging from a peg. we take the zero potential energy at the pivot. Homework Equations :[/B] http://www.physicsmynd.com/?p=1172The Attempt at a Solution Since the potential energy is zero at the pivot, and the...

Why is carbanion stability directly proportional to s character?

I think this should be my last question :D It's a question i missed on my last exam and have no idea how to do it and I wanted to quickly go over because my final is in a few hours so if anyone could help that would be awesome View image: 20151215 092327

Homework Statement Consider the dynamical system: $$\dot{r}=-ar^4+ar^3+r^6-r^5+r^2-r~;~~\dot{\theta}=1$$ Find all fixed points and limit cycles for: a) ##~~a=2## b)##~~a<2## c)##~~2<a<2\sqrt{2}## Homework Equations Not applicable. The Attempt at a Solution For all three values/ranges...

Homework Statement I have a simple writing assignment where my professor has asked us to write a couple pages about: - What a nano particle is, and the physics of how it's structure remains stable. The first part I've got covered. It's the structure part that's throwing me off. This is a...

A couple questions, please: I know that the Lagrangian points 1, 2 and 3 are unstable and special Lissajous orbits plus some station-keeping are required to place a spacecraft around them. But I was wondering if they are so totally unstable that they can't temporarily "capture" a passing...

Hi, Is this Bode diagram tells that the system is stable? As I see it is, because of the φ>0. What doest it mean that the upper diagram has two zero-crossing?

Homework Statement Homework EquationsThe Attempt at a Solution Hello, In part (b), I found ##k_{cu} = 0.5##. I found in part (d) a controller gain of ##k_{c} = -0.3## yielded a diverging output. Here are the bode plots for parts (a),(c), and (d). I don't understand how I should use the...

Hi, Consider the conservation laws for an isothermal linear incompressible flow governed by the mass and momentum equation. The kinetic energy equation is then solved to see if energy conserved. Can anyone tell me if once it is shown energy is conserved, it implies that convergence is obtained...

Hi everyone. I have here a problem understanding the stability of heat transfer through radiation. I'll give you some background, and later on I'll describe the physical problem. Background I am simulating the unsteady radiative heat transfer between mutually visible surfaces of objects through...