Nonlinear Definition and 558 Threads

Adapt the fortran programming using second order adams bashforth method to generate a numerical solution of the Lorenz system: dx/dt =-10x+10y dy/dy=28x-y-x*z dz/dt= x*y- (8/3)*z with initial condition x(0)=y(0)=0, z(0)=2 slightly perturbed. Plot x and z against t runs from 0 to 15, and also z...

Dear All, I have following first order nonlinear ordinary differential and i was wondering if you can suggest some method by which either i can get an exact solution or approaximate and converging perturbative solution. \frac{dx}{dt} = 2Wx + 2xy - 4x^{3}\frac{dy}{dt} = \gamma \, (x^{2} -...

Hello I want to ask you about the split method used to solve the nonlinear schrodinger equation numerically I just want to know what are the results that I am expecting to get how many graphs ??

Homework Statement Solve the System of DEs: \sqrt{1+y'^{2}+z'^{2}}-\frac{y'^{2}}{\sqrt{1+y'^{2}+z'^{2}}}=C_{1} \sqrt{1+y'^{2}+z'^{2}}-\frac{z'^{2}}{\sqrt{1+y'^{2}+z'^{2}}}=C_{2} Homework Equations The two equations above are quite relevant. The Attempt at a Solution I...

Hello awesome physics people! Someone asked me for help on their first year physics homework, and I couldn't really solve it. This kept bugging me, because I should know how this works by now :P Homework Statement See attachment for the full problem statement. Basically, a bow is strung with...

Hello, can you guys help me please with this differential equation from Demidovitch book, is to find the solution transforming to polar coordinates :

Homework Statement Solve the aforementioned system of nonlinear equations using Newton's method. write a program to carry out the calculations (it must use gauss elimination). Use the values 0-3 for x_{1}^{(0)}, x_{2}^{(0)} (ie. 16 data sets total). The Attempt at a Solution...

Hi there, I'm trying to find a calculation to work out the speed of erosion and required rotation of water to cause erosion on a selection of 10 rocks. This is theoretical rather than an actual conducted experiment. Each rock has a density of 100 to 1000, ie rock one is 100, rock 2 is...

Dear All, Recently, I have measured a series of nonlinear vibrational spectra from which I would like to extract some useful information about kinetics of the exchange process occurring in the studied system. I need to fit my experimental data to kinetic model that is a solution of coupled...

Hello, I am trying to find the effective resistance of the NLR in the attachment (to the first order). It is given that IL = gVL2 + I0. I understand that this is normally achieved via ∂g/∂V at V=V0, but when I do so I get that R should be 1/(2gV0), and not 1/2g as shown in the solution. Could...

hii, how to solve this differential equation: A*(dT(x)/dx)(1873.382+2.2111T(x))=90457.5-2.149*10^-10* (T(x))^4 where A is a constant Thank you

I am doing a little research project into numerical methods of solving ODEs where I do 1 half of learning about the basics of numerical methods and then look at a particular method (Linear multistep) and then the second half is looking at a particular example, applying what I've learned and...

In my work I've encountered equations of the type: (Ax).*(Bx) + Cx = d Where A,B and C are non-unitary square matrices, x and d column vectors and .* denote component-wise multiplication. I have a few books which discuss nonlinear matrix equations, but not of this kind. Any suggestions?

Homework Statement a) Find a mechanical system that is approximately governed by \dot{x}=sin(x) b) Using your physical intuition, explain why it now becomes obvious that x*=0 is an unstable fixed point and x*=\pi is stable. Homework Equations \dot{x}=sin(x) (?) The Attempt at a Solution...

I'm trying to create a java application that models the path of a double pendulum. To do so I have been attempting to use Lagrangian Mechanics to find the equation's of motion for the system. The problem is that I have never seen a set of equations like the one yielded by this method and need...

Hello! It is the first time that i write on this forum. I'm doing a PhD but i can't solve this equation: it's a non-linear second order differential equation. ay''+b|y|y'+cy+dx=0 Some ideas?

Hi everyone, new member zeroseven here. First, I want to say that it's great to have a forum like this! Looking forward to participating in the discussion. Anyway, I need to solve a pair of differential equations for an initial value problem, but am not sure if an analytical solution exists. I...

A function is additive if f(x+y) = f(x) + f(y). Intuitively, you might think that an additive function on R is necessarily linear, specifically of the form f(x) = kx. But assuming the axiom of choice, that is wrong, and the proof is rather simple: you just take a Hamel basis of R as a vector...

Homework Statement Given the equation \ddot{\theta}=\Omega^2\sin{\theta}\cos{\theta}-\frac{g}{R}\sin{\theta} Determine a first-order uniform expansion for small but finite theta. Homework Equations Other than the equation above, none so far as I am aware. The Attempt at a...

Hello, I need to minimize {- f (x) | a <=x <= b} where f ( x) is a concave and twice differentiable function. In addition, a and b are positive constants such that a <b. Assume that -f (x) exists in the given interval [a, b] . Show that if the optimal solution is at x*= a , then delta f...

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...

I let Mathematica run for over an hour but it couldn't solve this equation. Can someone run this in Matlab or Python and see if they can get a solution? $\alpha = 2\arcsin\left(\sqrt{\frac{10014.6}{2*a}}\right)$ $\beta = 2\arcsin\left(\sqrt{\frac{10014.6 - 6339.06}{2*a}}\right)$ $$...

Hi all, first post :) I have a system of z-propagated nonlinear PDEs that I solve numerically via a pseudo-spectral method which incorporates adaptive step size control using a Runge-Kutta-Fehlberg technique. This approach is fine over short propagation lengths but computation times don't...

Can someone give an example of a nonlinear operator on a finitely generated vector space(preferably ℝn)? I'd be particularly interested to see an example of such that has the group property as well.

I encountered the following second order nonlinear ODE while solving a problem in electrostatics. The ODE is: \frac{d^{2}V}{dx^{2}} = CV^{-1/2} How can I solve this? Regards. Homework Statement Homework Equations The Attempt at a Solution

Homework Statement See attached image Homework Equations Classification of critical points chart (unless you remember it) The Attempt at a Solution See attached. Now, I'm not entirely sure what exactly I'm doing. With linear systems, the goal is to find the eigenvectors...

The 3 equations are: 3xy-2xz=-1, -xy-xz=-1, -2xy+3xz=2 I've never learned how to solve these nonlinear equations. Is there anyway to solve this? I tried wolframalpha, but this was the result: http://www.wolframalpha.com/input/?i=3xy-2xz%3D-1%2C+-xy-xz%3D-1%2C+-2xy%2B3xz%3D2

Preface: just want to start by saying that I'm 99% sure I'm having a stability issue here in the way I'm implementing the time step since if I set \Delta t \ge 1 then for any stopping time > 1, the algorithm works as it should. For time steps smaller than 1, as the time step gets smaller and...

[Wasn't sure if each problem needed a separate post. Please feel free to edit if needed.] Also \~ and \^ are tilde and hat respectively. 1a. Homework Statement Use perturbation theory to derive the 3rd order nonlinear susceptibility \chi^{(3)}(3w;w,w,w) (problem gives potential energy, etc...

a = xyz b = xy+xz+yz c = x + y + z How do you solve x, y, and z?

Homework Statement (y^2 + xy)dx - x^2dy = 0 The Attempt at a Solution Put it into derivative form. y^2 + xy - x^2 \frac{dy}{dx} = 0 \frac{dy}{dx} - \frac{y^2}{x^2} - \frac{xy}{x^2} = 0 \frac{dy}{dx} + \frac{-1}{x}y = \frac{1}{x^2}y^2 I recognized this as a Bernoulli equation...

Homework Statement Verify whether or not the operator L(u) = u_x + u_y + 1 is linear. Homework Equations An operator L is linear if for any functions u, v and any constants c, the property L(c_1 u + c_2 v) = c_1 L(u) + c_2 L(v) holds true. The Attempt at a Solution I feel...

hi, I have some confusion for performing nonlinear analysis in ANSYS with NLGEOM... I was following the tutorial, the APDL is given below /prep7 ! start preprocessor /title,NonLinear Analysis of Cantilever Beam k,1,0,0,0 ! define keypoints k,2,5,0,0...

Hi everyone, I've got an optimisation/computing question. I have a system of nonlinear equalities and inequalities, which I've written below for reference. It's the conditions for a minimiser of a Karush-Kuhn-Tucker problem. Would anyone be kind enough to explain how I could use software to...

Take for example a system \frac{dx_i}{dt}=(x_i,t,a,b,...) i-number of state equations. What would be the maximum number of parameters permitted for this system of non-linear differential equations? Is it finally determined by the solution space?Is there a criteria for number of...

Homework Statement http://www.freeimagehosting.net/t/9369y.jpg Homework Equations The Attempt at a Solution a) is as follows: http://www.freeimagehosting.net/t/4oqft.jpg Then for b), I have the equilibria as (0,0,0) and (r-1,\frac{r-1}{r},\frac{(r-1)^2}{r}) To...

I need to solve the following ODE: http://www.sosmath.com/CBB/latexrender/pictures/041ee1419e05bc0776451b294c1dcc0e.png but i can't figure out a way to. Please help!

I need to solve 2 ODEs: 1. http://www.sosmath.com/CBB/latexrender/pictures/7b213e6c9e4d5fd9d92877694610ac22.png 2. http://www.sosmath.com/CBB/latexrender/pictures/528f96046147932945da54b7a47f97a9.pngbut i can't figure out a way to. Please help!

What is the solution of the follwoing differential equation \frac{\partial^{2}y}{\partial x^{2}}-ay^{-1}\frac{dy}{dx}=0 where a is a constant.

Hello, my question is that almost all textbooks say that a linear system will give the output to a weighted sum of impulses which equals the superposition of scaled responses to each of the shifted impulses. But if we apply the same input which is a weighted sum of impulses to a non linear time...

Strogatz's Nonlinear and Dynamics book states that $$ \langle\sin^{2n}\rangle = \frac{1\cdot 3\cdot 5\cdots (2n-1)}{2\cdot 4\cdot 6\cdots 2n} $$ for $n\geq 1$. However, $\langle\sin^6\rangle = \frac{5}{16}\neq\frac{15}{48}$. What is the deal here?

Hello everybody! While solving some physical problem I got stuck with some system of integral equations. The problem is formulated in .pdf file below. I will be over-satisfied with the following 1) to know whether and why this system has/doesn't have a solution 2) how it could be...

Homework Statement How do you derive the time-dependent velocity equation for motion along a curve, such as a skateboarder on a half pipe? For the sake of abstraction, I ask myself the following: A uniform sphere of mass m and radius r is set free from the top edge of a semicircle half pipe...

Show that all vector fields on the line are gradient systems. This is exercise 7.2.4 in the book "Nonlinear Dynamics and Chaos" by Steven H.Strogatz Thanks very much!

Homework Statement We have the equation: y'(x)^2+2 (x+1) \left(y'(x)+x\right)+2 y(x)+2 x=0 2. The attempt at a solution None. I don't even know how to proceed with this problem, except for, of course, expansion. I tried the factorization method, but no luck here. I have a feeling I...

Homework Statement Show that the following nonlinear system has 18 solutions if: 0 ≤ α ≤ 2∏ 0 ≤ β ≤ 2∏ 0 ≤ γ ≤ 2∏ sin(α) + 2cos(β) + 3tan(γ) = 0 2sin(α) + 5cos(β) + 3tan(γ) = 0 -sin(α) -5cos(β) + 5tan(γ) = 0 using the substitutions x = sin(α) y = cos(β) z = tan(γ) The Attempt at a...

Homework Statement given: dt=-\frac{1}{2}\sqrt{\frac{l}{g}}\frac{d\theta}{\sqrt{sin^2(\alpha/2)-sin^2(\theta/2)}} make the change of variables sin(\theta/2)=sin(\alpha/2)sin(\phi) to show that: dt=-\sqrt{\frac{l}{g}}\frac{d\phi}{\sqrt{1-k^2sin^2(\phi)}} where k=sin(\alpha/2) Homework...

The basal metabolic rate (in kcal/day) for large anteaters is given by: y=f(x)= 19.7x0.753 where x is the anteater's weight in kilograms a) find the basal metabolic rae for anteaters with the following weights i. 5kg ii. 25kg My answer: i= 66.19kg ii= 222.39 kg Hopefully I got a right...

I am having a problem finding the solution for this eq: y''(x)+(2/x)y'(x)+(w^2)y(x)=0 I couldn't find examples in the textbook that goes on a similar line, and have been searching the internet as well, but no use. I am thinking of using substitution v=y' but not sure how to do that in the...

Not sure if this topic belongs here, but here goes. Homework Statement From the AP physics C 1995 test there is a problem that gives the potential energy curve U(x). With F=-\frac{dU}{dx} in one variable, F(x)=-\frac{a}{b}+\frac{ba}{x^{2}} Where a and b are constants. Now I need to get...