Non-linear Definition and 318 Threads

Homework Statement Determine if the following set of equations has unique solution of the form ##g(z)=(x,y)## in the n-hood of the origin. $$\begin{cases} xyz+\sin(xyz)=0 \\ x+y+z=0 \end{cases}$$ Homework Equations I assume I am supposed to use the implicit function theorem...

Hi PF! Anyone have any ideas for a solution to this $$0 = F F''+\left.2F'\right.^2+ xF' + F$$ where primes denote derivatives with respect to ##x##. So far I have tried this $$0=\left( F F'\right)'+\left({xF}\right)'+\left.F'\right.^2$$ Which obviously failed. I also thought of this...

Hi, rank newbie here, with my first post. This one is something I figure every first year student comes up with at some point, but I don't know enough keywords to Search for an answer. (I'm not a student except in the category "of life": this isn't assigned homework) I figger, using a bit of...

Hi everbody My plots seem to show that conductivity between two nails immersed a few mm in tap water falls off at low voltages instead of being a horizontal flat line as would be the case for a linear ohmic medium. And the deeper the immersion, the less linear the conductivity. Is this normal...

i am finding it difficult to get insight about modelling of non linear system (electrical). my queries are, consider the system is DC DC converter... 1) I read that to study the dynamics of the system we linearise the non-linear system...why do we want to linearise it?... 2)can some one please...

Good morning everyone. First let me thank you for your help in advance! I have to solve this 2nd order non-linear ODE, and I'm stuck at the beginning. We have to find the equilibrium points, linearize the system, draw the phase portraits and classify the eq points, and solve it numerically. I...

I often create LED arrays, and have encountered a common issue where, as the LED load is increased, the total current requirement is not a linear factor as each branch (LED strip) is added to the circuit. It is common to have many branches of LED strips on a 12VDC 60W power supply. Power...

Homework Statement These questions are related to an experiment where we had to record the current for varying values of potential difference (10 readings), then repeat the process with the applied potential difference was reversed a) Why is the resistance of a light bulb not constant? b) Does...

What are the best book out there to learn about wave dynamic in Non-linear and dispersive media?

Common sense would suggest that all observed properties in a linear system would likely be linear. The response of a pendulum to an impulse can be computed, and for multiple impulses, the individual solutions can be superimposed to obtain the resultant solution. Qualitatively however...

What can you recommend as a non-linear load? Preferably one that can be bought or constructed inexpensively. Thank you!

Hello. I have some questions regarding the equation: k\frac{\partial}{\partial x}\left( u\frac{\partial (u-r(x,t))}{\partial x} \right) = \kappa \frac{\partial u}{\partial t}. u is positive. r(x,t) is given as an input. I have implemented this non-linear diffusion equation using backward Euler...

Hey guys, I'm going to be honest and say I'm so stuck on this assignment - I really need help! I've took on a third year computational physics course last year - turn your weaknesses into strengths someone told me. Well, I failed and I'm back doing it again this year! So, I just have to pass...

Homework Statement Please see the attached.I don't know how to do (ai). potential function is the potential energy defined by f = -dV/dx e is the total energy of the system where e = KE + PE = (dx/dt)^2 /2 + V Note:m=1 because the particle has a unit mass If you integrate f,you get V(the...

Hello, I am working through Hughston and Tod "An introduction to General Relativity" and have gotten stuck on their exercise [7.7] which asks to prove the following non- linear wave equation for the Riemann tensor in an empty space: ∇e∇eRabcd = 2Raedf Rbecf − 2Raecf Rbedf − Rabef Rcdef I have...

I have an extremely messy system of differential equations. Can anyone offer any ideas for a general solution? p(t) is a function of t, and A is a constant.

Hi, Please note: this is not a homework question! It is a real world problem I am trying to solve. I have some values in mA and tonnes which I need to extrapolate but they are not linear. I know it the mA curve drops off the higher the tonne values go. I have plotted the values in excel...

Hello every one . If the derivative is a linear operator ( linear map ) Then what is the example of non-linear operator Thanks .

Hi PF! Can any of you help me reduce this ODE to find a solution? $$y y''+2y'^2+xy'+\frac{1}{2}y = 0 \implies \\ (y y')'+y'^2+xy'+\frac{1}{2}y = 0 \implies\\ (yy')'+(xy)'+y'^2-\frac{1}{2}y=0$$ but here I am stopped. Am I even going the correct route? I know I can re-write this equation as...

Hello My question could be about bars and litres/sec but I'll express it as volts and ampères, mathematically it's the same puzzle for me. How do you calculate the currents in circuits when there are devices whose resistances are not linear? In the following network there are 3 low value linear...

Hello! (Wave) I want to find the solution $\psi$ of the non-linear differential equation $y'=1+y^2$ that satisfies the condition $\psi(0)=0$. (Notice that the solution $\psi$ exists only for $- \frac{\pi}{2}< x < \frac{\pi}{2}$) We notice that: $(tan^{-1})'(x)=\frac{1}{1+x^2} (\star) \left(...

Hi PF! I have a system of nonlinear ODE's, wherein the only constant ##C## in the ODE takes on several values depending on the geometry; thus once a geometry is defined for the ODE, ##C## is uniquely determined. Let's say I want to guess a quadratic solution to the ODE, call it ##\phi(x)##...

Hi PF! I am wondering if any of you have experience numerically solving second order ODE's? Basically, I'm trying to solve one and am trying to do it numerically in mathematica. Can anyone help? For those curious, the equation is ##y y'' + 2y'^2 +xy' = 0## where ##y## is a function of ##x##...

Homework Statement $$y' y + \frac{y}{x} = 1 - 2x$$ Homework Equations nothing comes to mind The Attempt at a Solution i've guessed a quadratic but that didn't work. now I'm stuck. any ideas? also, this is not homework, but a problem I am working on. Thanks!

Homework Statement find the vector with magnitude 5 and perpendicular to 3i-2j+4k and 4i-3j-kThe Attempt at a Solution lets name the vector component x for the i y for the j and z for the k i got three equation 1- x^2+y^2+z^2=25 ( magnitude) 2-3x-2y+4z=0 3-4x-3y-z=0 (2, 3 from dot product by...

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...

It seems to me that there are many instances of 'initial stickiness' when you move an object. Pushing a book over a table for example might be initially hard due to adhesive forces to the table which have formed over time - a plastic coating forming some kind of seal with a varnish is the...

From the diagram above, there are two types of wires a straight wire and a non-straight wire(zig-zag shaped wire), that are both placed inside a magnetic field(B), and have current flowing in both of them as well. The straight wire will experience a force and will move towards the left as...

I've decided to finish off this stage of my GR problem by finding an interval over which the acceleration of the object is "roughly" constant. I don't need help with the Math per se, but I would like your opinion on the method I am proposing. The Math is sufficiently ugly that I'd like some...

If you really want to know where this comes from I am solving the GR equations for a rectilinearly isotropic metric. In other words, I can express the metric as d \tau ^2 = -T(x) dt^2 + X(x) dx^2 + dy^2 + dz^2. (It may be simpler to use a cylindrical coordinate system, but the equations come...

Homework Statement In this question we will consider a damped mass-on-a-spring system whose spring exhibits cubic deviations from Hooke’s law. We will consider a damped spring with a restoring force F such that F/m=−βx−αx^3 where β is the “Hookian” part and α is a new nonlinear term. Unlike...

Hi all. I'm really at a loss on how to find the "other" points of intersection for this system of equations: x^2-y=4 x^2+y^2=4 Obviously we have a parabola and circle. I have solved for x and got "2", and plugged that back into get "0". However the answer has 4...

Hy I want to know how to make linearization for some function,...what should by in Non-linear least squares problems. In my book I have only this example how to do: http://i.imgur.com/MUFiHkr.pngSomeone could me help how to do, some receipt of method what I need to do? Non-linear least...

Hi, i didnt know where to put this question cos its kind of multitopic, here is why... I am working on a better way to take mechanical energy from muscles, i made a teste bench for pedalling in very different ways, including traditional(circular) pedalling, the thing is. I am measuring the power...

It is said that a non-linear optical device may convert light into its higher order components. So what is the highest efficiency of the conversion? Can a non-linear device convert all input light into its higher order frequency? Thanks.

For the non-linear sigma action, S_G=\frac{1}{4\pi\alpha^\prime}\int d^2\sigma\sqrt{-\gamma(\sigma)}\gamma^{\mu\nu}(\sigma)G_{ij}(X)\partial_\mu(\sigma) X^i\partial_\nu X^j(\sigma), Let us consider an infinitesimal target space transformation X^\mu\to X^{\prime\mu}(X)=X+\epsilon\xi^\mu(X). The...

I need to design a CAM composite with a spring for an exoskeleton to aid elderly mobility. However, the problem I face right now is that the CAM I designed provides a linear force profile, i.e., the force varies proportionally with the extension of the leg. How can I delay this force applied so...

(r^2) (dT/dr)+B*r*T=T^2, with initial condition dT/dr |r=0 =0 where B is a constant I've gotten it to this: dT/dr = -BT/r + T2 / r2 by dividing everything by r2, then I substitute using λ= T/r which gives: r * dλ/dr + lambda = -B * (λ) + λ^2 I don't know how to separate...

I have some questions about this paper:http://users.phys.psu.edu/~radu/extra_strings/freedman_sigma_model.pdf In section 3, they renormalize the bosonic non-linear \sigma model at one loop level. The action is given by I_B[\phi]=\frac{1}{2}\int...

Quick version: I have a vector field f:\mathbb{R}^n\oplus\mathbb{R}^m \to \mathbb{R}^n of two arguments x \in \mathbb{R}^n, y \in \mathbb{R}^m, which has the following properties: The jacobian matrix of f wrt to the first argument \frac{\partial f}{\partial x}: \mathbb{R}^n\oplus\mathbb{R}^m...

Hi. First off, sorry for the not so descriptive title. If one of you finds a better tilte I will edit it. We have the equation \begin{equation} \partial_{xx}\phi = -\phi + \phi^{3} + \epsilon \left(1- \phi^{2}\right) \end{equation} We will look for solutions satisfying...

Hi everyone. I am doing research about what happens to light energy after it has been absorbed by a leaf but before it has been used in the photosysnthetic reactions. For that I need to use system of 3 nonlinear ordinary differential equations. My dissertation title is : A hybrid numerical...

I am trying to solve 3 differentail equations(Lorenz equations) using ode solver: ode23s in Matlab. Here are the 3 lorenz equations: dc/dt= alpha*I*(1-c) + c*(- k_f - k_d - k_n * s - k_p*(1-q)) ds/dt = lambda_b * c* P_C *(1-s)- lambda_r *(1-q)*s dq/dt = (1-q)* k_p * c *(P_C /...

I am trying to solve 3 non-linear system of 3 variables using the Newton-raphson method in matlab. Here are the 3 non-linear equations: \begin{equation} c[\alpha I+ k_f+k_d+k_ns+k_p(1-q)]-I \alpha =0 \end{equation} \begin{equation} s[\lambda_b c P_C +\lambda_r (1-q)]- \lambda_b c P_C =0...

I am trying to solve 3 non-linear system of 3 variables using the Newton-raphson method in matlab. Here are the three equations: \begin{equation} c[\alpha I+ k_f+k_d+k_ns+k_p(1-q)]-I \alpha =0 \end{equation} \begin{equation} s[\lambda_b c P_C +\lambda_r (1-q)]- \lambda_b c P_C =0 \end{equation}...

1. Is there a general condition for the existence and uniqueness of solution of a system of simultaneous non-linear equations similar to the determinant test for a system of linear equations. 2. What are the solution methods (theoretical and numerical) for solving a system of simultaneous...

The three non-linear equations are given by \begin{equation} c[(6.7 * 10^8) + (1.2 * 10^8)s+(1-q)(2.6*10^8)]-0.00114532=0 \end{equation} \begin{equation} s[2.001 *c + 835(1-q)]-2.001*c =0 \end{equation} \begin{equation} q[2.73 + (5.98*10^{10})c]-(5.98 *10^{10})c =0 \end{equation} Using the...

Hello everybody. Solving a problem in Physics I run into a system of equations that I do not know how to solve, I would appreciate some help. Here is the system: \ddot{x}+4\dot{x}^2=C_1e^{y} \dot{y}^2=C_2\ddot{x} The dependent variables are x,y. C_1 and C_2 are some constants. I try...

Here is the question: I have posted a link there so the OP can view my work.

Am am presented with the problem: $$ h(t) = c - (d - 4t)^2 $$ At time t = 0, a ball was thrown upward from an initial height of 6 feet. Until the ball hit the ground, its height, in feet, after $$t$$ seconds was given by the function $$h$$ above, in which $$c$$ and $$d$$ are positive constants...