On the many different ways to turn non-linear systems of equations into linear ones.
Questions tagged [linearization]
349 questions
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Can I linearize a System of SDE without losing the constant terms?
I have the following system:
$dx/dt = con_1 + a_1k_1y - k_1x$
$dy/dt = con_2 + b_1k_2x + b_2k_2x^2- k_2y$
that I want to linearize.
However, I'm not able to do it properly, because my aim is to linearize the system, estimate the parameters (of the…
Huaweu149
- 11
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1 answer
Clarification of Linear Equation of Motion to Determine Stability
I am working through a problem of a bead moving without friction on a surface $z=f(r)$ in cylindrical polar coordinates $(r,\theta,z)$, under the influence of gravity. I have shown that $h=r^2\dot\theta$ is constant and that
$$(*)\;\;\;\large…
jcneek
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For what values of x is the linear approximation $\sqrt{x + 3} \simeq \frac74 + \frac x4 $accurate to within 0.5?
For what values of x is the linear approximation $\sqrt{x + 3} \simeq \frac74 + \frac x4 $accurate to within 0.5?
My Try
I found this question under llinearization lesson
Since this problem does not mention about a point around which it is…
emil
- 1,310
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1 answer
Linearization of $a(x^b)(e^{cx})$
I'm working on an assignment and I need to solve the equation $y=a\times(x^b)\times(e^{cx})$.
We're given an array of values for $x$ and their corresponding $y$. We need to figure out $a$, $b$, and $c$.
My instructor gave us the hint of linearizing…
K.Jay
- 11
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3 answers
Linear Approximation of x/ (1-x)
I am trying to linearize the following function, but, having difficulties.
Let,
$x = \frac{l}{m},$
where $l,m \in R^+$ and $l
tcokyasar
- 147
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I can't understand linearization
I'm having a course on control theory and some problems require linearization. It's not that we focus much on it. It's usually just the first question of a bigger problem so I'm just looking for a simple way to do it.
Let's take this for example:…
John Katsantas
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Is it correct to linearize a part of a differential equaztion?
if I'm not wrong, if I have a differential equation like this:
$Dl=a_0k_1 + k_1a_1x + k_1a_2x^2 - k_1l$
and I want to linearize it, I can linearize only the quadratic part (ergo, $k_1a_2x^2$ ). Right?
But then, when I carry out the linearization…
Huaweu149
- 11
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Linearization to estimate uncertainty
Consider a cone of height H and diameter D
Use linearization to estimate the allowable percentage error in the measurement of D if the colume of the cone is to be determined to within 2% of its true value?
So I know you are supposed to differentiate…
Jisbon
- 79
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divide complex finction in to multiple linear functions
im programing a small controler an have to use sqrt but the controler doesnt suport it . the controler have what they call a 24 point linearization wich means that you chose 24 x and y positions and the controler makes 23 linear functions out of…
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Linearization of a function: can someone explain me this last step?
I'm studying a linearization of a differential equation. $x(t)$ and $r(t)$ are really small signals and G, K, B and M are constants. I understand everything until I reach
$$ \frac{d^2x(t)}{dt^2}=G+\frac{K}{M}\sqrt{\left|…
Granger Obliviate
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Linearizing two variable function
I have another linearization question similar to the one in here. This time, I have got two variables in my equation and I am in search of an "$A+B\rho$" or possibly "$A+B\rho+C\theta$" approximation. Here is my equation:
$$W =…
tcokyasar
- 147
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Linearizing Logarithmic Function
I have a given set of data points (y,x) with uncertainties.
When I plot those points on a graph, the trendline appears to follow the equation y = c + a*ln(x).
I want to be able to find the uncertainty in "a".
So just like linearizing an exponential…
선풍기
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How do I linearize this?
I'm given the following and I 'm asked to linearize around $x_1=0,x_2=0$$$x_1=x_2^2 \\ x_2=e^{x_1}+u$$
Only thing I know how to do is find the value for $u$ which is $-1$. The only problems I've faced are similar to this one I can't understand…
John Katsantas
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Linearization of an equation
I came across an exercise about the linearization of this non-linear equation arount the operational points $x^{\circ}=0, y^{\circ}=0$:
$$y=a\ddot{x}+b\sin x$$
The process started by:
$$x=x^{\circ}+\Delta x,\; \dot{x}=\dot{x}^{\circ}+\Delta…
Adam
- 351
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Diameter increase approximation (Linearization)
The diameter of a tree was 10 in. During the following year, the
circumference increased 2 in. About how much did the tree’s
diameter increase? The tree’s cross-section area?
we are using linearization to predict the increase as you can see in the…
