## Linearise differential equation...

Dear all,

I have to differential equations that I'd like to linearise, that is all higher order (>1) derivatives (like diff(uu[0],x\$2)) and parameters (like beta^2) and the products of any derivatives with the parameters uu[0] and beta are zero (as they are assumed small).

The two equations considered are displayed below:

Up to now, I perform a very tedious substitution which is based on looking at the equations above and decide which terms I want to get rid of. Something like this, where K =1:KFBCLin:=simplify(eval(KFBC, [beta^3 = 0, beta^2 = 0,
seq(subs((diff(uu[n], x\$3)) = 0),n=0..K),
seq(subs((diff(uu[n], x\$2)) = 0),n=0..K),
seq(subs((diff(uu[n], t))*beta = 0),n=0..K),
seq(subs((diff(uu[n], x))^2 = 0),n=0..K),
seq(subs(g*diff(beta, x)*beta = 0),n=0..K),
seq(subs((d^2*diff(uu[n], x,t)*diff(beta,x)=0)),n=0..K),
seq(subs(-2*d*diff(uu[n], x,t)*beta*diff(beta,x)=0),n=0..K),
seq(subs((d^2*diff(uu[n], x\$2,t)*beta=0)),n=0..K),
seq(subs((diff(uu[n], x)*uu[n])=0),n=0..K),
seq(subs((diff(uu[n], x)*uu[n]*beta)=0),n=0..K),
seq(subs((diff(uu[n], x)*uu[n]*d)=0),n=0..K),
seq(subs((diff(beta, x)*uu[n])=0),n=0..K),
seq(subs((diff(uu[n], x)*beta)=0),n=0..K)]));As there is a lack of automatisation, this procedure is not very helpful. Life would be easier if there was a command (or the like) that says "get rid of higher order derivatives".Any help is appreciated.Best regards,

## How can linearization be done with maple...

How can one use maple to linearized nonlinear ODE of this type Linearize.mw

with maple.

Best regards.

## Linearizing differential equations...

Hi! I was wondering if anyone knows of a way to taylor expand an expression around a function. For example, let's say I have an expression like

expression := diff(f(r), r\$2) + exp(-f(r))*(1 - g(r))^2

and I want this expression to be linear order in f and g. If I try

mtaylor(expression, [f(r), g(r)], 2)

I get an error. I don't want to replace f(r) with just f (for example) because then all of the derivative terms vanish, and I want this to also be of linear order.

## Linearization tool in API...

The code behind "Linearize" button in the Linearization template is as follows:

The results, namely A,B,C,D matrices in the state-space presentation, are shown in the text area "mcEqs".

How can I save these matrices to some variables for further analysis?

In addition, without the linearization template,

## How to conventionally build/generate msys system o...

Hello all,

I'll be straight-forward.

I have Maple 15+MapleSim 5. I don't have Control Design Toolbox. I want to embed a linearized system object as an msys file into MapleSim.

The Linearization template failed to create the file. I tried to use the codes in the template directly as code in Maple, but also failed. Seemingly because I don't have Control Design Toolbox in which the code need to load.

I have been googling around with no avail. I...

## How to extract affine terms from a differential eq...

How to extract affine terms from a differential equation after linearization?

Vanderpol Eqn:

To be precise, I linearized...

## Linearize and extract the linear matrix solution...

Hey,

I have linearized the following system and I want to extract the linear matrices (a,b,c,d) form the solution. The program is as follows:

## Extract linear matrices from StateSpace...

Hey,

I am trying to linearize a Statespace and extract the linear matrices from the solution. Using following example, can you explain how to extract the matrices a,b,c,d.

## Help on linearizing a system......

Hi everyone,

I've been able to generate equations of motion for my system. I want to linearize the obtained equations. How to do it? I've been trying to find some example on it, however, haven't been lucky as yet. Can anyone please help me with this? Anticipating a quick reply!

Regards,

Moazzam

## Command to Linearize an PDE non-linear...

Is there any command in Maple 15 to linearize an PDE non-linear? Or or there is a package or help file to do so?

I'm handling with Non-linear PDEs in my work and I would like to solve them by these methods.

Thank You

Washington Inacio

## How to linearize three nonlinear equations?...

Hello friends,

I have tried to linearize three nonlinear equations which are coupled in the form of:

a1*xdot(1)+a2*xdot(2)+a3*xdot(3)=f1(x1,x2,x3)+u(1)

b1*xdot(1)+b2*xdot(2)+b3*xdot(3)=f2(x1,x2,x3)+u(2)

c1*xdot(1)+c2*xdot(2)+c3*xdot(3)=f3(x1,x2,x3)

the ai, bi, ci parameters are constant parameters and x1, x2, x3 are variables (states). also, u(1) and u(2) are inputs to the system. xdot(i) is the derivative form of xi.

## Equations of motion to state space...

Hello:

I am in need of help with Maple Linearize and an exremely crypitc and most un-helpful error message. What does this mean:

> linmod := Linearize(syss, parm, linp);
Error, invalid input: Linearize uses a 4th argument, linpoint (of type {list(`=`), set(`=`)}), which is missing

I can find nothing in the help in this.

Linearize works fine when running a sample program from the help files, but fails when I run my equations.

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