MaplePrimes - answers and comments on Question, Simplifying a vector expression with composite functions

Simple example

Preben Alsholm — Wed, 13 Feb 2013 21:03:56 Z

Here is a simple example, which probably just shows that I don't understand your problem:

restart;
with(LinearAlgebra):
M:=<seq(m[i](t),i=1..3)>;
H:=<M[2],M[1],M[3]>; #Simple example
eqs:=diff~(M,t)+ M &x H-a*M &x diff~(M,t)/DotProduct(M,M,conjugate=false)=~ <0,0,0>;
sys:={seq(eqs[i],i=1..3)};
res:=dsolve(eval(sys,a=1) union {m[1](0)=1,m[2](0)=0,m[3](0)=0}, numeric);
plots:-odeplot(res,[seq([t,m[i](t)],i=1..3)],0..10);

Thanks a lot for your answer. In fact, I

PlpPlp — Wed, 13 Feb 2013 22:46:21 Z

Thanks a lot for your answer. In fact, I don't want to solve the equation, but simply make it look better (this is to check my calculation). Furthermore, my H is defined as the derivative of a function with respect to the m_i, which are functions of t, and maybe I was doing things the wrong way but Maple didn't accept what I suggested to him. Therefore, I decided to discard the variable t and keep only the small perturbations of the m_i as variables.

Attached is my worksheet so that you can understand if you have just some time (as well as my initial problem which was not clearly explained!) Now, I have everything that I want, but I'm looking for a way to:

- linearise the last result (i.e. keep only constant terms, x-terms, y-terms, z-terms and discard all the multiple variable terms). I checked on the online help and I could only found a Linearize function that works for systems, not really what I'm looking for.

- group the terms so that the result looks like: (constant terms) + (coefficients)*x + (coefficients)*y + (coefficients)*z. Is there any of doing so easily?

Again, thanks a lot for your help.

Download resonance.mw

Maybe this?

Preben Alsholm — Thu, 14 Feb 2013 21:31:01 Z

@PlpPlp I changed things a little to reflect my understanding of the problem. I use worksheet interface and 1D input (so much easier for me).

DeltaF := K[1]*m[1]^(2)*m[2]^(2)+(K[1]+(B[1]^(2))/(2* c[11])-(B[2]^(2))/(2 *c[44]))*(m[1]^(2)+m[2]^(2))*m[3]^(2)+K[2]*m[1]^(2)*m[2]^(2)*m[3]^(2)+B[1]*(u[m1]*m[1]^(2)+u[m2]*m[2]^(2))+B[2]*u[m6]*m[1]^(2)*m[2]^(2)-B[1]*((B[1])/(6 *c[11])+(c[12])/(c[11])*(u[m1]+u[m2]))*m[3]^(2)+1/(2)*mu[0]*M[s]^(2)*(N[1]*m[1]^(2)+N[2]*m[2]^(2)+N[3]*m[3]^(2))-mu[0]*M[s]*(H[1]*m[1]+H[2]*m[2]+H[3]*m[3]);

H[eff1] := -diff(DeltaF, m[1])/mu[0];
H[eff2] := -diff(DeltaF, m[2])/mu[0];
H[eff3] := -diff(DeltaF, m[3])/mu[0];

expr := collect(mu[0]*(m[2]*H[eff3]-m[3]*H[eff2]),[m[1],m[2],m[3]],distributed,factor);

#Now linearising about m = m0. The number 2 at the end means that the orders neglected are 2 and above.

mtaylor(expr, [m[1]=m[1,0],m[2]=m[2,0],m[3]=m[3,0] ], 2);

Perfect

PlpPlp — Sat, 16 Feb 2013 16:12:28 Z

@Preben Alsholm This is exactly what I needed, you're a life saver and I begin to understand how Maple works. Thanks a lot.