Nonlinear Definition and 558 Threads

Homework Statement Hello everyone. I'm trying to solve a non linear 11x11 system. (for eliminate harmonics in a power inversor) I used Excel's Solver but it didn't work. (Solver couldn't solve the system). Then I found fsolve (a scilab function) but again it didn't work I will attach...

Homework Statement \frac{dy}{dx}=\frac{2y - x + 7}{4x - 3y -18} Homework Equations The Attempt at a Solution I tried using v = y/x and got nothing. Same goes for trying to find an integrating factor to make the equation exact. I am given a hint, Find h and k so that the...

Hello, I am confused as to how to transform nonlinear ODEs to linear ones by change of variables. Usually its pretty straight forward and I can do it, but this particular problem has me stumped and I don't know where to begin. Homework Equations Thank you guys!

I'm having trouble understanding the exponential map for nonlinear vector fields. If dσ/dt=X(σ) for vector field X, then how does one interpret the solution: σ(t)=exp[tX]σ(0) ? If X is nonlinear, then X is not a matrix, so this expression wouldn't make sense. If X is a...

I'm trying to solve a system of five nonlinear equations (degree 7) in Mathematica: Solve[{q (a^2 + b^2 (3 q^2 + r^2 + 8 t^2)) ((e - q)^2 - R^2 - 4 T^2)^2 + q ((e - q)^2 + R^2 + 4 T^2) - 2 (e - q) (r R + 4 t T) == 0, R (a^2 + b^2 (3 R^2 + (e - q)^2 + 8 T^2)) ((e - q)^2 -...

1. y''y^4 = 8 I tried almost every method I know, including laplace transforms, variation of parameters, reductin of order, v=y' substitution

I saw this post at stackexchange: I ran across this post when trying to solve a homework problem. But I have no idea how he got that solution for that. When I use the Euler-Lagrange, I get this diff eq below. Here is the simplest form I have managed to get it in...

Hi Everyone I tried all ways I can to solve (y^2+x^2+x)y'-y=0, but still cann't find a way to solve it. Could anybody help on it? Thank you very much!

Hi all, I've got a nonlinear differential equation of the general form y' + f(x)y + g(x) = h(x)(y^n) to solve. For g(x) = 0 this is your standard Bernoulli equation. I've been trying to think of a way to solve it but haven't managed so far. Any ideas would be appreciated. Many...

Homework Statement Is this differential equation linear or nonlinear? Assume that y' means dy/dx. Homework Equations 1. Homework Statement [/b] Is this differential equation linear or nonlinear? Assume that y' means dy/dx. Homework Equations \sqrt{xy'+2x2}=5 The Attempt...

Homework Statement I want to find the general solution for y(x) if dy/dx = x + y^2 with initial cond't y(1) = 2 Homework Equations The Attempt at a Solution I can't figure out how to make it linear. (Obviously I don't think it's seperable) Any suggestions/solutions...

Hello! I am taking a self study diff e course, and I have run into a problem with no one to ask for help. Here is the problem: d/dt [ h^3(t) + 3h(t)^2 + 3h(t) ] = q(t) h(t) is output. q(t) is input. is this Nonlinear First Order Differential Equation. But I could not expand to...

I was wondering what the common methods for solving such a system are: 2 m \ddot{x} - m l \ddot{θ} θ + k x = 0 m l^{2} \ddot{θ} - m l \ddot{x} θ + m g l θ = 0

Lately I have been reading about nonlinear systems and chaos. It's fascinating and I would like to know more about how I could prepare myself to possibly study this in grad school. I would be interested in looking at biological systems such as neural networks or even animal populations. I'm a...

Like linear algebra goes in depth about linear systems, what should I look for to learn about the extension of linear algebra to nonlinear systems? Is there a name of the field of study? If I go into a book store to buy books about it, what should I be looking for? Abstract Algebra? Complex...

Hi, My understanding that one of the postulates of quantum mechanics is that the vector describing the quantum mechanical state of a system evolves in a linear fashion. My question is how this can be reconciled with systems where the system evolves in a non-linear fashion for example systems...

I am not too familiar with differential equations but am familiar with basic calculus, I came across this equation trying to describe a particular function: dy/dx =((sqrt((y-x)^2+y^2)-abs(y))/(y-x))*abs(y)/y Anyway I tried to separate the variables unsuccessfully and using v(x)=y(x)/x with...

Hi I like to fit in Mathematica using NonlinearModelFit. When I look at the fitted parameters, there is an entry called "P-value". Here is what it means: "The p-value is the probability of observing a t-statistic at least as far from 0 as the one obtained.". I'm not quite sure what this...

Hi, Part of my research, I nondimensionalized an ODE to eventually arrive at this form: sin(τλ) = q^((n+2)/(n+1)) + κq' + q'' where q' = dq/dτ The problem is of course the nonlinear q^n. n is an integer greater than 0. Is there a Laplace transform for this? Or what solutions are there for...

hi all, I've been trying to work this problem out, \frac{dv}{dt}-A(B-v)^{1.6}=G A, B and G are constants and Matlab can't give me a solution either. I'm wondering if there is even a solution?

A problem from a heat transfer book with conduction and radiation led me to a differential equation like this: T'(t) = a - b*T(t) - c*T(t)^4 Although my professor said that there wouldn't be an analytical solution for this one and to get the answer by an iterative method I got curious and...

Homework Statement \ddot{y} = - \dot{y} - y -sin(y) Homework Equations The Attempt at a Solution to reduce the order I need to find a solution y1. it seems to me the only obvious solution is y1 = 0 but i can't use this to do a reduction can i

I've been reading through my mechanics of materials textbook recently, notably in regard to the section on the deflection of beams. The well regarded Euler-Bernoulli beam theory relates the radius of curvature for the beam to the internal bending moment and flexural rigidity. However the theory...

Hi everyone, I am trying to solve an optimization problem using fmincon in Matlab with a nonlinear inequality restriction. Part of the objective function is undefined if this nonlinear inequality is violated. I also set up lower and upper bounds for fmincon. I use the "interior-point"...

Consider the equation \frac{a_n-a_{n-1}}{1+a_na_{n-1}}=\frac{1}{2n^2} I know one special solution is a_n=\frac{n}{n+1} But how to solve and find the general solution? Thanks in advance.

Ok, to start off I have been examining the structure of polynomials. For instance, consider the general polynomial P(x)=\sum^{n}_{k=0}a_{k}x^{k} (1) Given some polynomial, the coefficients are known. Without the loss of generality...

Ok, this should be quite simple. I've been looking at this problem for quite some time now, and I'm tired.. Please help me! The equation to solve is r' = r(1-r^2) The obvious thing to do is to do partial fraction expansion and integrate(from r_{0} to r): ∫ (\frac{1}{r} +...

Hey, I need your help to solve the following set of coupled differential equations numerically. dn(t,z)/dt=I^5(t,z)+I(t,z)*n(t,z) dI(t,z)/dz=I^5(t,z)-α(n(t,z))*I(t,z) where I(t,0)=I0*exp(-4ln2(t/Δt)^2) and n(t,0)=0 and n(-certrain time,z)=0. Some constant parameters I did not show...

Homework Statement Consider the following differential equation: x^{2}\frac{dy}{dx}=x^{2}-xy+y^{2} State whether this equation is linear or nonlinear and find all it's solutions Homework Equations I think that the Bernoulli differential equation is relevant, but I'm not sure...

Is it possible to solve the following differential equation analytically? y''(x) = A - B [exp(y(x)/C) - 1] where A, B and C are constants. Thank you...

Homework Statement A wire 60 feet long is cut into two pieces. Is it possible to bend one piece into the shape of a square and the other into the shape of a circle so that the total area enclosed by the two pieces is 100 square feet? If this is possible, find the length of the side of the...

Hi all, It seems to me that the derivation of Maxwell stress tensor is independent of the permeability of the media or the nonliterary of its B-H relation. By this I mean that we use μ0 in the equations rather than μ. Would you please confirm that?

Homework Statement In one problem I had got to this equations, but I was not able to solve it, because I'm actually on high school. The equation : d^2/dt^2(x) = -h*g/(h+x) I tried use separation of variables but I was not able to use the chain rule. Can anybody show me the steps...

Hi Does nonlinear conductive liquid metal exist? Which and where? thx

Hi all, I have a nonlinear differential equation and I need to find an analytic solution for it. Here it is: \ddot{S}=-{1 \over 6} \dot{S}-{2 \over 7}(1-S)^2(- \dot{S})^{1.3} I have used a transformation to simplify it: -\dot S = v and came up with this DE which I couldn't solve...

Hello to everybody, I'm very new to solving ODES and equations with MATLAB. I have been asked to solve a system of nonlinear equations for simulating the growth of a solid tumor. Assuming that we have the 5 unknowns which are dxd arrays: f,g,m,p and n. f(x,t) is the volume fraction of tumor...

Practice Problems to "Nonlinear Dynamics..." Strogatz Book Hi, I'm taking a dynamics course which uses the "nonlinear dynamics and chaos" book by Strogatz. I get a half-descent understanding from the lectures of the prof and the book's explanations of things, but \ is\ there\ a\ good\...

Hello. I have simple DE y' + p y^(1/2) = q --------------- y'=dy/dt p,q=constant I am confused because I tried bernoulli's method to solve and I think I exploded the universe. Basically, my initial condition of t=0,y=0 made infinity, not right. I'm not sure that method works when there...

hey guys i've been trying to work out this ode reduction question, http://img204.imageshack.us/img204/8198/asdawt.jpg after i use the hint and end up with a seperable equation then integrate to get \begin{align} & p=\pm \frac{1}{\sqrt{{{y}^{2}}-2c}} \\ &...

A "simple" nonlinear ode Hi Does anyone see a way to solve/approximate this ODE? dy'=exp(-f(t)y) with y(0)=yo f(t) can be as simple as c*t^3/2 but it may be more complex. This came out as the solution of a very complex problem. This is the final threshold. Thanks, Donifan

Hello, It's my first topic here. :) In order to solve a PDE numerically, I have reached in a nonlinear system of algebraic equations. Does anyone here know a good method to solve it numerically? It seems like this: xij (t+dt) is proportional to xi,j+1(t), xij2(t), xi,j-12(t)...

Homework Statement Consider the system x' + x = F(t), where F is smooth, T-periodic function. IS it true that the system necessarily has a stable T-periodic solution x(t)? If so, Prove it; If not, find an F that provides a counterexample. Homework Equations x' + x = F(t) The...

Basically where are nonlinear dynamics and chaos theory used in the real world? Like if someone studies it what type of areas might they find it being useful for? The only example I can seem to think of is stuff like weather/fluids/air resistance/physics. What might be some other more...

Hi guys, I have been reading up on the KdV equation and everywhere it states that the waves need to be 'weakly nonlinear and weakly disspersive.' From a physical point of view does this mean that the wave amplitude must be small? If that is the case how would one model large solitons...

if we are given a polynomial s^6+as^5+bs^4+cs^3+ds^2+es+k (if a,b,c,d are known) what is a clever method to solving for the value k if we are given the following: the above polynomial is equal to the following(zeta is given as some constant, say 1 for simplicity)...

Nonlinear loads produce odd harmonics which produce square waves. What will happen if a square wave is pulsed into a nonlinear load? Would the same square wave be seen across the load or would the nonlinear load change the square wave? If a capacitor is nonlinear (i.e. capacitance...

As the thread title says I'm interested in Chaos Theory, Complex Systems, and Nonlinear Systems. If I can help it, I'd like to study these at graduate level. My question is what kind and how much mathematics I'm supposed to know if I'm to study these?

I've been looking at nonlinear control system and fuzzy control in particular. If I simply want to do trajectory control (have the system to follow a certain trajectory in phase space), can I use much simpler local linear control? I mean, for each point in phase space, do a local...

Homework Statement Inverted pendulum on a cart on a frictionless surface, write the state-space description of a nonlinear system. outputs are theta(t), theta'(t), y(t), y'(t). Everything is 2-dimensional. Homework Equations theta(t) is the angle between the gravity vector and pendulum y(t)...

Hi, I need some help to find the analytical solution of the following DE: x" - k x/x' = at + b, with x' = dx/dt and x" = d(dx/dt)/dt Any kind oh help or advices on where I can find some useful resources are really appreciated. Thank you