Linearizing Definition and 34 Threads

Summary:: Linearizing an equation for MILP Hi All I have Linear programming problem where I need to linearise the following function: Y = A * log2(1 + (Bx/Cx^2)). where A, B and C are constants. Can you please help or advise?

I started by substituting the following anzatz: $$ \psi = \psi_e + \psi_1 $$ When ## |\psi_1| \ll 1 ##. Substituting the above into the equation yields: $$ \frac {d\psi_1} {dt} = -(1 + i\alpha)\psi_1 + \frac i 2 \frac {\partial ^ 2 \psi _1 } {\partial x ^ 2 } + i (\bar \psi_1 \psi_1 ^2 + \bar...

Homework Statement For a single mechanical unit lung, assume that the relationship among pressure, volume, and number of moles of ideal gas in the ling is given by PA((VL)/(NL)a = K, where a = 1 and K is a constant. Derive the lowest-order (linear approximation to the relationship among changes...

Homework Statement So these are the equations of motion for a quad-copter. I am supposed to create a MATLAB model for the z-axis. In order to do this I have to linearize the equations around these points, and arrange them in state space representation. Homework Equations As above The...

Hi! Above is a screenshot of logger pro that I'm currently using. I need to linearise this graph and draw a best fit linear line but I have no clue how to do it. What should I do? The table on the left shows the raw data. The first column is showing the values for x-axis, and the second is for...

Hi everyone. I started to look at different linearization techniques like: -linear interpolation - spline interpolation - curve fitting... Now Iam wondering (and I guess its very stupid) : As polynomials with a degree > 1 are not linear, why can I use them for linearization? With the...

Hi all! I am taking an online course on aerial robotics and am currently on the topic of linearizing a 2-D quadrotor dynamic model. See slide (link below): The equations under "linearized dynamics" are derived using the equilibrium hover configuration (e.g. y = y0, z = z0, Φ0 = 0, u1,0 =...

I am given the equations of Lorenz with respect to deterministic non-periodic flow: \frac{dX}{dt} = Pr(Y-X), X(0)=X_{0} \frac{dY}{dt} = -XZ + rX - Y, Y(0) = Y_{0} \frac{dZ}{dt} = XY-bZ, Z(0) = Z_{0} where Pr is the Prandtl number, r = Ra/Rac is the ratio of the Rayleigh number to its...

Homework Statement I posted the entire question, but I am only conserned with part B. There was a circuit drawing on there but it is irrelevant for this part of the problem. One can solve it without knowing the circuit drawing. Homework Equations The application for Kirchoff's Voltage Law...

I am linearizing a vector equation using the first order taylor series expansion. I would like to linearize the equation with respect to both the magnitude of the vector and the direction of the vector. Does that mean I will have to treat it as a Taylor expansion about two variables...

Homework Statement I did a lab this week measuring periods of swings of a simple pendulum. We need to curve fit the equation T=k*l^n and we got ln(T)=n*ln(l)+ln(k), and we need to plot the data we collected into the linear graph, meaning out y axes is ln(T) and our x axes is ln(l). So far all...

I have a nonlinear least squares problem with a set of parameters \bf{g}, where I need to minimize the function: \chi^2 = \sum_i \left( y_i - M(t_i ; {\bf g}) \right)^2 The t_i are some independent parameters associated with the observations y_i and the model function has the form M(t_i ...

Homework Statement I have all of the data but I just can't find the equation to linearize it. X values: 0, 1.98, 3.96, 5.94, 7.92, 9.9, 11.88 Y values: 1.98, 7.13, 9.08, 11.04, 12.57, 14.51, 14.342. The attempt at a solution I know it is not a parabola, cubic, exponential, or inverse.

Homework Statement Use a suitable substitution to transform the nonlinear DE (dy)/(dx)+y=y² into a linear equation in the new variable z. and without solving the DE, justify the possible methods that can be used to solve the DE found in first part. Homework Equations I have no idea what to...

Homework Statement The goal of my lab was to measure the ratio of charge to mass for electrons (e/m) and the approximate ambient magnetic field of the Earth (BE). I have come up with what is the required equation (my TA confirmed this) but I am having trouble linearizing it. y=mx+b...

Greetings~ We were told to linearize this equation below: y= x^2/(a+bx)^2 after we multiply both the sides with the denominator (a+bx)^2, and then divide both the sides by y, can we apply ln to both the sides? Because I can see no other way of linearizing this :/

Homework Statement Rolling Motion Theoretically, a=⅔g sin θ suggests a nonlinear relation between a and θ. Since a linear graph is a very convenient method of testing theoretical equations, it is a good idea to first linearize a=⅔g sin θ. A simple way to do this is to assign a as the...

Homework Statement The viscous passage of gas through a capillary from a region (Region 1) to another (Region 2) is described by Pouseuilles' Law. I have to find a way to linearize Pouseuilles' law such that I can have a linear equation where the slope is dependent on the viscosity of a gas...

Hi everyone! I have an issue with my physical chemistry lab. They ask us to rearrange the fallowing equation v=vw + (v0 - vw)e^-kt where v is velocity and t is time, vw is a constant They also ask which quantity would be plotted as ordinate and as absissa. We have to indicated the parameter...

Homework Statement Consider the following implicit scheme: y_{n+1}=y_{n}+\frac{\Delta t}{2}\left [f(y_{n+1})+f(y_{n})] By linearization one can obtain an explicit scheme which is an approximation to this - with approximation error O(\Delta t^{3}) Homework Equations The solution is...

This question popped up while trying to solve problem 7.41 from Taylor's Classical Mechanics book. Basically we have the differential equation (1+4k^2\rho^2)\ddot{\rho} = \rho \omega^2 - 4k^2\rho{\dot{\rho}}^2-2gk\rho and we are looking if the equilibrium position \rho = 0 is stable...

Linearize and classify the fixed points of \frac{d\theta1}{dt} = \Omega + sin \theta1 + \frac{1}{2} (sin\theta1 + sin\theta2) \frac{d\theta2}{dt} = \Omega + sin \theta2 + \frac{1}{2} (sin\theta1 + sin\theta2) I know that if the absolute value of omega is less than two, there will be 4...

so i have the function z=(2+i)/(i(-3+4i)) and i need to linearize it to find the Im(z) and Re(z) I get down to z= (-6 +8i -3i -4 )/ (9i +12 +12 -16i) which i then simplify down to z= (5i -10)/(-5i+24) However when solve it i get a different answer from wolfram (from when i plugged...

Hi, I'm working on a project (not homework) where I have to linearize a set of non-linear equations of motion They take the form: x_dot(x,u) = B(x)*u + A(x) where A and B are functions of state vector x. x_dot is a time derivative of x. A - n x 1 B - n x m u - m x 1 (wish I...

Hi guys, I am trying to linearize a coupled non-linear ode. I used partial derivative, and then jacobian matrix, i have seen paper using state-space model of jacobian matrix. I can't get a proper reference on this state-space model. Attached is the non-linear ode, the partial derivative of the...

Homework Statement I am modeling a set of equations for a protein network. It is a feedback loop between 2 proteins. I have gotten the differential equations for this model and plan on doing an extended Kalman Filter to estimate the levels of protein in real time. However, I am having...

Homework Statement I make the product \cos(x)\cos(5x) a sum of two cosines. I think this is called linearizing but please correct me if I'm wrong. (I need it to find the n-th derivative of that function). Homework Equations The Attempt at a Solution I know the answer is...

Homework Statement Hi, I need to produce a linearized equation of the following, I = D. V. exp(-V/B) eq(1) I is the current V is the voltage D is a constant B is a constant Data was collected in an experiment designed to investigate the characteristics of a...

Homework Statement How do you linearize a parabolic graph? the parabolic graph is obtained from an experiment relating to projectile motion. Angle (tan) Average Displacement 20.11 15.72 24.3 18.84 28.98 20.4 38.29 21.68 49.67 18.9 61.53 18.44 74.6 10.18 This is the...

hello, I'm doing coursework on using a thermistor as a temperature sensor. For my preliminary readings I had to choose between 3 different thermistors. Is it true that, for example, a 22k thermistor has a resistance of 22kohms at 25 degrees? (my tutor told me this) likewise, a 15k thermistor...

Homework Statement I want to linearize both the Stefan-Boltzmann equation and the adiabatic relation to draw a relationship between δL/L(0) and δR/R(0). Homework Equations Stefan-Boltzmann equation in the form of L=4πσ(R^2)(T^4) Adiabatic relation TV^(γ-1) = constant The Attempt at...

Homework Statement basically I am suppose to linearize d=vit + 1/2at^2 into d/t^2 vs 1/t, t/d vs t^2/d and 1/d vs 1/t and its asking which graphs would be linear and non-linear. Homework Equations d=vit + 1/2at^2 The Attempt at a Solution all i know is that in order to linearize this i...

Homework Statement Linearize the system operator illustrated below by applying a Taylor series expansion. f(t) ----> e^f(t) -----> g(t) Homework Equations I only find the general form of a taylor series relevant. g(x)= sum (0,infinity) of [f^n*(a)*(x-a)^n]/n! The system is...

Well this is a physics related question but I think putting it in math is best. I am trying to linearize the doppler shift function of light. I know that means to expand it and take the linear terms but don't really know what to do. I was guessing a taylor series expansion but...