Stability Definition and 524 Threads

Hi everyone I'm taking a linear algebra class at university right now and this is one of my homework questions . I am unsure how to even approach these questions. Any pointers in the right direction would be greatly appreciated. I apologize in advance for not showing any attempt at this...

So is a Bike driver stable when the bike is running because the bike wheels has a certain moment of inertia about the horizontal axis ,which might alter(mi gets lesser) if the direction of the axis changes ? Thanks in advance

I was recently taught the concept of nuclear forces in school.According to what was taught,nuclear forces were introduced to explain the stability of the nucleus.So,my question is that,can't we say that the nucleus is stable only due to neutron-proton and proton-proton interactions?Why are...

Homework Statement Homework EquationsThe Attempt at a Solution part a[/B] $$ \vec {x} = \left [ \begin{array}{ccc} X-X_{s} \\ S-S_{s} \end{array} \right ] $$ $$ \vec {u} = \left [ \begin{array}{ccc} S_{0}-S_{0s} \\ \frac {F_{0}}{V}- \big (\frac {F_{0}}{V} \big )_{s} \end{array} \right ] $$...

Homework Statement A solid cube of side ##l = r*pi/2## and of uniform density is placed on the highest point of a cylinder of radius ##r## as shown in the attached figure. If the cylinder is sufficiently rough that no sliding occurs, calculate the full range of the angle through which the block...

Hello, I have a typical 1D advection problem where a cold fluid flows over a flat plate. I did an energy balance to include conduction, convection and friction loss and I got the PDE's for the fluid and the solid. I used finite differences to solve the system as T(x, t) for both fluid and...

As per control theory, if a bounded input produces a bounded output then a system can be said to be stable. So assuming that I press my cars gas pedal such that it reaches a fixed position, then the reaction of my car would be to reach a corresponding velocity, and assuming the road to be even...

Hello. I've studied the golden rules of the feedback OP-AMP and applying this to voltage follower shows that voltage gain (Vout/Vin) is 1. Thus, Vout should eventually follows Vin when Vin suddenly changed. I've tried to follow this process for clear feeling by drawing pictures as shown in the...

Hello! (Wave) The following Runge-Kutta method is given. $$ \begin{array}{c|ccccc} \tau_1 =0 & a_{11}=0 & a_{12} = 0\\ \tau_2 =\frac{5}{2} & a_{21} = \frac{5}{2} & a_{22} = 0\\ \hline & b_1 = \frac{4}{5} & b_2 = \frac{1}{5} & \ \end{array} $$ I have to determine the order of accuracy and...

Hello! (Wave) I am looking at the following exercise.We suppose that the explicit Euler method is applied at the differential equation of second order $\left\{\begin{matrix} x''(t)+(\lambda+1)x'(t)+ \lambda x(t)=0\\ x(0)=1\\ x'(0)= \lambda-2 \end{matrix}\right.$ $$|\lambda|>>1$$ What step...

So, from what I can tell, anything that is formed from heavier flavors of particles (strange/charm quark, top/bottom quark, muons, taus, etc.) is incredibly unstable, to the point of top quarks only ever being observed indirectly through its decay products. Anyway, I was wondering, is this the...

Hi There! How a neutron is able to make a nucleus stable?

Hi, I know, there is a stability condition for solving the Convection-Diffusion equation by Finite Difference explicit/implicit technique, which is \Delta t<=(\Delta x)^2/(2*D) for one-dimensional or \Delta t<=((\Delta x)^2+(\Delta y)^2)/(8*D) for two-dimensional problem, where D is the...

Now a days in most of the power systems(generation,transmission (HVDC, HVAC) and distribution) we use semiconductor devices for efficient use of power.using power electronic components in power systems does it affect the stability(transient/steady state)?

Hello! (Wave) We have the problem $$\left\{\begin{matrix} y'=\lambda y &, t \in [0,+\infty), \lambda \in \mathbb{C}, Re(\lambda)<0 \\ y(0)=1 & \end{matrix}\right.$$ Applying the Backward Euler method $y^{n+1}=y^n+h \lambda y^{n+1}$, we get that $y^n=\frac{1}{(1-h \lambda)^n}$. So that the...

I need to do this graph "graphic locking range and stability laser" that equations are used to make the graph thanks

I am working on proving that an equilibrium point of a two-dimensional dynamical system is globally asymptotically stable. The background and justifications are below. I have gotten to the final steps (in bold), but cannot justify it. It seems right intuitively. Can someone navigate the argument...

Homework Statement Does +I effect stabilize or destabilize a carbocation Homework Equations NA The Attempt at a Solution In one way, +I effect tends to increase electron density on the carbocation and hence neutralize the charge and hence would stabilize it. On the other hand, the nature of...

Hello! (Wave) We have to look for numerical methods for the numerical solution of $\left\{\begin{matrix} y'(t)=f(t,y(t)) &, a \leq t \leq b \\ y(a)=y_0 & \end{matrix}\right.$ that have 'great' regions of absolute stability. Methods of which the region of absolute stability contains the whole...

How does the nucleons losing some of its mass energy help in making it more stable?

Hi friends, this is my third post of my curiosity. :woot: First of all a photonic vacuum (as defined by me) is a region of space where there doesn't exist any type of photons or EM radiations ( those too which are beyond the detection of our present tech... i.e. including each and every...

Consider: prop-1-enylbenzene Why is the carbocation more stable when the +ve charge is on the carbon directly attached to the benzene ring as apposed to the +ve charge on the the 2nd carbon counted from the benzene ring?

I have read that if pole of a function or say , a system lies in right half of a s-plane , then the system is unstable..! But I did'nt get the logic behind it..! What's the reasn of system being unstable if pole is lying in right half..?? Please elaborate...!

Hello All, I need some explanation on the relative stability of 237-Np and 237-Pu. We know that 237-Np has 2.144x10^{6} yrs of half-life. On the other hand, 237-Pu , which has only 1 extra neutron as compared to 237-Np has a half-life of 45.2 days with EC and alpha as most prominent decay...

I was looking at some interesting resonant orbits in our solar system and was wondering if someone who knows a lot more about planetary orbits than I might be able to answer if a certain scenario would actually lead to stable orbits or not. The scenario I have in mind is four planets tightly...

Generally, in organic reactions, the para isomer is found to be more stable (as it is symmetrical) because of which it is produced in greater amount than the ortho isomer. However, there are some exceptions also, for example, in some reactions the less sterically hindered ortho isomer is...

Homework Statement In a classical model of a multi-electron atom, electrons are assumed to move in a modified electrostatic potential $V(r)$, given by; $$V(r)=\dfrac{-k}{r}e^{-r/a}$$ Show that the effective potential is ; $$V_e(r)=\dfrac{J^2}{2mr^2}+\dfrac{-k}{r}e^{-r/a}$$ Then show that...

I am trying to make PDMS wells (50 um diameter, 100-200 um deep) and was considering using a SU-8 mould fabricated by lithography. This would however mean that I would be making 50um diameter/100-200 um high pillars. I am unsure about the mechanical stability of this system. Will the pillars...

Homework Statement (a): Show the lagrangian derivative in phase space (b)i: Show how the phase space evolves over time and how they converge (b)ii: Find the fixed points and stability and sketch phase diagram (c)i: Find fixed points and stability (c)ii: Show stable limit cycles exist for T>ga...

Homework Statement The attempt at a solution 1) Is the above excerpt describing pi-backbonding? It seems to be describing some form of backbonding because the electron density is moving away from the positively charged metal cation (rather unexpected based on superficial Columbic analysis)...

Homework Statement Where it says ''from the bottom'' I assumed it's referring to a distance along the ladder. So: Data: ##w_{ladder} = 98.0\ N## ##w_{person} = 686\ N## ##d_1 = 4\sqrt(2)\ m## ##d_2 = 1\ m## ##d_3 = 2/3\ m##Homework Equations ##\sum \tau = 0## ##\sum F = 0## The...

Homework Statement Find whether this system is stable or unstable at the steady state (x1,x2)=(0,0) dx1/dt = -x1+2sin(x1)+x2 dx2/dt=2sin(x2) Homework Equations The Attempt at a Solution z1=x1-0 z2=x2-0 dz1/dt=-z1+z2+2z1 dz2/dt=2z2 Jacobian = [ 1 1 ] [ 0 2 ] so the system is unstable. This...

Homework Statement Data: ##m = 500\ kg## Distances given in the image. Homework Equations ##\tau = rF\sin(\theta)## ##F_{net} = ma## The Attempt at a Solution It seems this problem is intended to be one where torque applies, but I don't see it in that way. And of course my answer...

Ok I know this should be easy but it's been a few years since my physics lessons at college and I'm stumped. I work in packaging. I'm working on a tool that will tell me if a box will fall over when it is subjected to an edge drop test. That means that a block is placed under one edge of a box...

In many cases one finds code such as x = linspace(-3,1.5,200); y = linspace(-3.5,3.5,200); [X,Y] = meshgrid(x,y); Z = X +Y*i; %Euler's Method M = abs(1+Z); [c,h] = contour(X,Y,M,[1,1]); set(h,'linewidth',2,'edgecolor','g') to plot the stability region of the Euler's Method, where in fact the...

In central motion we have criteria for stability. For function of force f(r) we have stability if f'(r)+\frac{3}{r}>0 This is stability in what sence? Do I have then periodic orbits or what? Is it in some connection with calculations of Lyapunov exponent? Thanks for the answer.

Homework Statement The figure below shows the path of a particle governed by the Lorenz equations with r = 28, σ = 10, b = 8/3. The x'es and boxes show points where the path crosses the plane z = r − 2σ > 0. (a) Which indicator shows a decreasing z and which shows an increasing z? (b) Show...

Q: A structure is made from identical, axially compressible robs connected to a rigid foundation. The rods cannot buckle. In the unloaded configuration the angle between the rods and the horizontal is (alpha); then angle becomes (1-Beta)*alpha when p =/= 0. Find the relationship P(Beta)...

Greetings, I am interested in creating a thread dedicated to the discussion of the uses of currently discovered and used and theorized/dreamed of types of matter in our universe. This includes R.E.E's (Rare Earth elements, like Neodymium or Yttrium...

Hi, I'm considering the energy evolution of variables of different orders in a partial differential equation. The PDE is nonlinear, which can be written as ## \frac{\partial u}{\partial t} = \mathcal{N}u ## where ##\mathcal{N}## is a nonlinear operator in space and time. Now I want to check...

I know that the criterion of stability for an explicit solution to the heat equation: \frac{\partial T}{\partial t}=D\frac{\partial^2 T}{\partial x^2} is \Delta t <\frac{1}{2}\frac{\Delta x^2}{D} however, what is the stability criterion for an equation of the form \frac{\partial T}{\partial...

Which carbocation is more stable? 1) CH3-C+=CH2 2) CH3-CH+-CH3 Basically, I want to know whether the =CH2 group is electron donating or electron withdrawing. Does it show +I effect like alkyl groups? I mean, like in 2) the carbocation will get stabilised due to the electron donating power of...

Hi Physics Community, I'm working on the design of an aileron less and tail engine small UAV (Wing span 800mm) but I got stuck in Stability and Control. I recall from a teacher that a V-tail design is good for those configurations. However, I cannot find references to calculate/estimate neither...

Hi everyone, I know that classical mechanics and electromagnetism show that the electron is bound to fall on the nucleus. I want to estimate the duration of the phenomenon. I found the classical energy : E=-K/r and I'm able to compute the raying loss thanks to electromagnetism. But I am...

Hi All I have done transient stability simulations on isolated electrical network using ETAP 7.5 software. Problem: On buses Faults generators return to stable stade But on cable faults, rotor angle is diverged so the system is not stable. To be noted that we have 2 SOLAR generators of 5MW...

I'm doing research with my professor on H-Bridge Power Inverters, I noticed that the more load we put on the device the better the wave looked (by better I mean cleaner, not as much noise). By ohm's law the current should be falling; would this not happen only if the current were rising? I...

I have a linear time-varying linearly perturbed ODE of the form: \dot{x} = [A(t)+B(t)]x where A(t) is a bounded lower-triangular matrix with negative functions on the main diagonal, i.e. 0>a^0\ge a_{ii}(t). The matrix B(t) is bounded, so that ||B(t)|| \le \beta. The question is...

Many fighter aircraft have anhedral on their wings - F-104, Dassault Mirage III. What is the effect on control - is it neutral roll stability through 360 and more important, what is the effect on stability - is there a 'notch' effect if there is no dihedral where the aircraft tends to assume...

If uranium 238 is more stable than uranium 235 because 3 extra neutrons add to strong force then uranium 236 having 1 extra neutron should have more strong force than uranium 235 so why does it decay so fast and why is it more unstable than uranium 235?

dear sir, i am curious to know whether black hole can be broken apart by some means?