Stability Definition and 524 Threads

I am trying to understand attracting, Liapunov stable, asymptotically stable for given coupled system. I don't have any Liapunov function. Just two coupled systems such as ##\dot{x} = y##, ##\dot{y} = -4x## or sometimes normal systems ##\dot{x} = -x##, ##\dot{y} = -5y## How can I approach...

Not sure if this off-topic ,but I think it would fit in Stem Career guidance. I'm currently a 2nd year physics major in Thailand and have been losing sleep thinking about my future in academia for days. Yeah just like many of you guys here, I was inspired to pursue physics by many of great...

I was working on a proposal for a spacecraft , and suddenly realized that the ideal orbit may be a high inclination type of near-Earth coorbital called a "retrograde satellite" or RS orbit. Do you know of: * A person who can compute 100 years of coorbital stability using three body (sun...

The hint says that "The cross-section of the underwater part of the beam could be represented as a superposition of a rectangle and two symmetrically positioned narrow triangles (one of them of negative mass)." How do I find the torques from gravity and buoyancy on these figures?

As it's written in the following article, nuclear binding energy is always a positive number; thus it takes energy to disassemble a nucleus into its nucleons. ...The binding energy is always a positive number, as we need to spend energy in moving these nucleons, attracted to each other by the...

Dear community, I am an electrical engineer trying to make my hobby four seater car. Being not a mechanical guy I am really uncertain of the chassis design that I have concepted though with the help of a friend we got some basic simulation running. My concept is to use a standard rectangular...

Why is it that it is more stable for a negative charge to be spread over 2 oxygens than one oxygen and 3 carbon atoms? Following that logic, why is it more stable to spread a negative charge over 3 oxygen atoms than over 1 oxygen atom and one nitrogen atom? Is it because the difference in...

Hi everyone. I'm currently trying to master the use of the formula for nuclear masses from MYERS AND SWIATECKI (1969), https://www.sciencedirect.com/science/article/pii/0003491669902024. $$ E=[-a_1+J\delta^2+0.5(K\epsilon^2-2L\epsilon \delta^2 +M\delta^4)]A+c_2 Z^2 A^{1/3}...

Homework Statement y(t) = x(1-5t) Homework Equations noneThe Attempt at a Solution well I've never looked at the stability of a signal which has a time scale and shift. My guess is that it is stable as anything I can provide as input will output a bounded signal. Ex: if x(t) is u(t) then...

Hi, I'm reading a book about numerical models for PDE and it says that a method is said to be stable if this condition holds: $$|| \mathbf u^{n+1} || \le c_t || \mathbf u^{n} ||$$ where ##c_t## is a constant greater than zero, and ##u## is the numerical solution to the problem. (In particular...

Homework Statement [/B] (Solved. through the work on this post i found the mistakes) Most basic stability problems is introduced simply as a box with a load placed on its side. And you do the typical momentum calculation around the opposite edge. Most books/pdfs stops there. I have however...

Homework Statement The textbook "Organic Chemistry by O P Tandon" says that the tropylium cation (cycloheptatri-2,4,6-enyl cation) is more stable than the triphenylmethyl cation ( Ph3C+) (phase/solvent not mentioned). Is this correct assuming it's in a non-polar medium ? On a related note, are...

Hello; I import karting tires from Taiwan , while reviewing a sample tire sent for inspection for our order, I noticed a change in spec. of Duro rating . We spec. them at 65-75D ,this sample came in at 60-65D ..here is the factory response= Hi Gus, The tire factory explained that the tire...

I am working on a presentation for a course in general relativity and my topic is the stability of black holes. In many of the references and articles that I have found, the author asserts the importance of the conjecture but offers no reason. So I ask: Why is the black hole stability conjecture...

Homework Statement Give an example of a non-linear discrete-time system of the form x1(k + 1) = f1(x1(k), x2(k)) x2(k + 1) = f2(x1(k), x2(k)) With precisely four singular points, two of which are unstable, and two other singular points which are asymptotically stable. Homework Equations J =...

Hi, I'm an amateur observer of nuclear physics, so I'm curious about how larger and larger elements are produced in particle accelerators. Like for example, they've created elements all of the way upto element 118 now, I guess? Like when they get Plutonium from Uranium, do they bombard with...

<Moderator's note: Moved from a technical forum and thus no template.> Technically the homework question is at graduate level, but the area I'm having trouble on I feel is at an undergraduate level. In the question we studied a particle rotating on a vertical hoop that is also rotating about...

Homework Statement This is a conceptual question I have, the binding energy per nucleon is mass defect*c^2/mass number while the packing fraction is mass defect/mass number. A higher binding energy per nucleon indicates a more stable nucleus BUT a smaller packing fraction indicates a more...

Homework Statement Among the following, which should be the most stable compound? 1)Cis-cyclohexane-1,2-diol 2)Trans-cyclohexane-1,2-diol 3)Cis-cyclohexane-1,3-diol 4)Trans-cyclohexane-1,3-diolHomework Equations -- The Attempt at a Solution My thought process is-cis isomers with adjacent OH...

In a previous message I have tried to show that electrical systems exist which do not generate electromagnetic waves with appreciable energy even if such systems have parts in accelerated motion. Now I add a further example by which the meaning of what I tried to say becomes clearer. The problem...

Imagine a steel I-girder lifted by a single wire rope. If the rope is not perfectly centered along the girder length, the girder will rotate about a horizontal latitudinal axis through its centroid. Imagine a girder pair lifted by two wire ropes, with one rope on each side of the girder...

First of all: excuse me for my not good english written language. I come to the question with an example. Let us suppose two electrons are in space with initial velocity equal to zero. Given the Coulomb force such electrons will be submitted to an equal and opposite accelerations (for the action...

I have uploaded the picture of the structures because I couldn't figure out how to type. Its vinyl chloride. According to me the order should be I>III>II because I has no charge so it must be most stable in II we have Cl an electronegative element bearing positive charge which makes it...

<< Mentor Note:Thread moved from the Homework forums because it isn't really about homework >> Preface With my limited understanding of physics, I am unaware of what section of the forums this question would fall into. I am not doing this for school(though possibly it might help with that in...

An LTI circuit such as one composed of resistors, capacitors, and inductors, in general is a stable LTI system, i.e. its impulse response is one that decays over time. I have no problem with that, as it speaks for itself through laws of energy conservation, but I want to see this from a...

Hello! I'm new to the Physics forums so I'm not too sure if this is the right place. But hopefully it is :) Anyway, I'm currently an IB student studying Physics at higher level and decided that I was going to do my EE (extended essay), which is about 4000 words, on physics. Since I really...

Homework Statement Question: Discuss what values of Z and N might give stabilty to a nucleus with A=22 Homework Equations $$BE=a_vA-a_sA^{\frac{2}{3}}-a_c\:\frac{Z\left(Z-1\right)}{A^{\frac{1}{3}}}-a_s\frac{\:\left(A-2N\right)^2}{A}+\delta \left(A,Z\right)$$ The Attempt at a Solution For this...

Dear colleagues: My name is Ignacio Pérez, a mining engineering student from Spain. I am trying to analyze the stability of a slab with rounded edges against a toppling failure. The slab can be considered rectangular-prism shaped (I provide a rectangular section in the enclosed picture) but the...

Hi, I am looking at the following system of ODEs: \begin{eqnarray*} \dot{\omega}_{3}+\alpha\omega_{3} & = & \frac{\beta_{1}+\beta_{3}}{\rho_{0}}J_{3} \\ \dot{J_{3}}+2(\alpha_{2}-\alpha_{1})\beta_{2} & = & 0 \\ \dot{\beta}_{1}+\omega_{3}\beta_{2} & = & 0 \\...

Homework Statement If a beam with square cross-section and very low density is placed in water, it will turn one pair of its long opposite faces horizontal. This orientation, however, becomes unstable as we increase its density. Find the critical density when this transition occurs. The density...

I want to build a bass guitar stand for my guitar using wood, I'm modelling it after the image shown. The alterations I'm making are to increase the height of the legs , to place an attachable weight below the stand . This will allow the stand to have a lower center of mass and will greatly...

Homework Statement [/B]Homework Equations Number of encirclements = Number of open loop poles - Number of Close loop poles on Right side of S plane. The Attempt at a Solution There is 1 open loop pole on RHS For Close loop poles I used Routh Herwitz method and got 1 pole on RHS. 1 sign change...

The enthalpy of formation of O3 is positive. Change in entropy for the formation of O3 is also negative( as the number of gaseous moles is decreasing). This means that Delta G is positive for all temperatures. So formation of ozone should be non spontaneous at all temperatures. Then how does it...

Homework Statement The equation x^2+3x-0.45=0 has two solutions x1=0.14 and x2=-3.14, these are supposed to be the locations at which the electric charge is in equilibrium with two other charges, should I use the first derivative to see at which location the charge will be stable? Homework...

Homework Statement I have a system of coupled differential equations representing chemical reactions and given certain initial conditions for the equations I can observe oscillation behaviour when I solved the equations numerically using Euler's Method. However, then it asks to investigate the...

Homework Statement I have a problem with question (b), in what follows there's a quote of the problem and its solution. (again from Bergersen's and Plischke's textbook). Homework EquationsThe Attempt at a Solution [/B] My problem is with the last expression in (d) I get 54 instead of 36. To...

Hi, Maybe someone remembers how to determine the necessary conditions for a static structure to be stable and not to roll over. I know about the method when you imagine the structure has been rotated back an forth, and depending on how the center of mass takes higher or lower state the...

Help with the question of the concept of the stability of the speed of light. I gather that current atomic clocks are based upon the speed of the electron around their nucleus, which is a function of the speed of light. Measurements of the speed of light that depend upon atomic clocks therefore...

Homework Statement In the ##(n,x)## plane, where is the recurrence stable for increasing ##n##? $$E_{n+1}(x) = \frac{1}{n}\left( \exp(-x)-xE_n(x)\right):E_n\equiv \int_1^\infty \frac{\exp(-xt)}{t^n}\,dt$$ and ##n\in \mathbb{N},\:x\geq0##. Homework Equations Nothing comes to mind. The Attempt...

I tried a cursory search for this but couldn't find it. I was talking with my advisor about 5D theories such as those of Paul Wesson and Randall-Sundrum, and he said that I shouldn't spend too much time studying those theories because they are unstable, or require so many corrections to...

I just watched this video that perfectly explains how to derive the equations for the slip angle of a car: However, how could this be done for a three axle system (car-trailer)? Would you have to express distance a (in the video) in terms of b (distance from centre of gravity to the second...

Homework Statement [/B] I am trying to identify every force in this system and prove that it is in mechanical equilibrium when tan(θ)=⅓. Initially I had to solve it by finding when the derivative of potential with respect to θ was 0, but now I am just trying to resolve the forces. Homework...

Hi Everyone I'm studying material Engineering and I'm currently preparing chemistry for the summer exams. Now, there is an old exam question which I don't know how to solve: "In which temperature range does ##[W^{+VI}F_{6}^{-I}]## melt?" My solution: Well, the 18-Electron rule is not...

We know that the lower the energy gap between bonding and antibonding orbital the easier it is to break the bond making it unstable. However, in a conjugated double bond, the overlapping of wavefunctions cause the energy gap between the bonding and antibonding orbital go down. Then why...

Im quite fascinated over how Earth is constantly trying to stabilise itself. What is your most interesting observation or 'happening' about climate change?

I'm reading a book on vortex methods and I came across the above mentioned terms, however, I don't understand what they mean in mathematical terms. The book seems to be quite valuable with its content and therefore I would like to understand what the author is trying to say using the above...

Let's say there's five Mars/Earth massed planets orbiting a star like the sun between 0.6 AU and 2 AU, what orbital resonance configuration can they be into ensure maximum stability? Would adding gas giants to the system enhance stability?

launching a missile from the water, how the ballast stability works?

Hey, is it possible to have a cylindrical ring (made of permanent magnet) and a magnetic sphere sitting inside it and staying in one place without touching the inner sides of the ring and not falling through? The object doesn't necessarily have to be a sphere. If it would work with any other...

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...