Quantcast
Channel: MaplePrimes - Questions and Posts tagged with solve
Viewing all articles
Browse latest Browse all 1089
↧

solving homogeneous algebraic equations for non-trivial solution

September 3, 2016, 1:42 am
$
0
0

Hi,

I am trying to solve a set of homogeneous equations for the non-trivial solutions. Mathematically it is possible to get it. But is there any way to get it in Maple. Please find the attached maple sheet for the question. Please help me regarding this.

Regards

Sunit

> 

restart

> 

with(plots):

> 

with(LinearAlgebra):

> 

eq[1] := diff(x[1](t), t)-x[2](t)

diff(x[1](t), t)-x[2](t)

(1)
> 

eq[2] := diff(x[2](t), t)+2*zeta*beta*x[2](t)+beta^2*x[1](t)+n*psi*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

diff(x[2](t), t)+2*zeta*beta*x[2](t)+beta^2*x[1](t)+n*psi*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

(2)
> 

eq[3] := diff(phi[1](t), t)-phi[2](t)

diff(phi[1](t), t)-phi[2](t)

(3)
> 

eq[4] := diff(phi[2](t), t)+2*kappa*phi[2](t)+phi[1](t)+n*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

diff(phi[2](t), t)+2*kappa*phi[2](t)+phi[1](t)+n*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

(4)
> 

for k to 4 do eqn[k] := simplify(coeff(map(expand, eval(eq[k], [x[1] = (proc (t) options operator, arrow; x[1]*exp(lambda*t) end proc), x[2] = (proc (t) options operator, arrow; x[2]*exp(lambda*t) end proc), phi[1] = (proc (t) options operator, arrow; phi[1]*exp(lambda*t) end proc), phi[2] = (proc (t) options operator, arrow; phi[2]*exp(lambda*t) end proc)])), exp(lambda*t))) end do

x[1]*lambda-x[2]

 

x[2]*lambda+2*zeta*beta*x[2]+beta^2*x[1]-n*psi*v*phi[1]+n*psi*v*phi[1]*exp(-2*lambda*Pi/(n*omega0))+n*psi*x[1]-n*psi*x[1]*exp(-2*lambda*Pi/(n*omega0))

 

phi[1]*lambda-phi[2]

 

phi[2]*lambda+2*kappa*phi[2]+phi[1]-n*v*phi[1]+n*v*phi[1]*exp(-2*lambda*Pi/(n*omega0))+n*x[1]-n*x[1]*exp(-2*lambda*Pi/(n*omega0))

(5)
> 

A, b := GenerateMatrix([seq(eqn[k], k = 1 .. 4)], [x[1], x[2], phi[1], phi[2]])

A, b := Matrix(4, 4, {(1, 1) = lambda, (1, 2) = -1, (1, 3) = 0, (1, 4) = 0, (2, 1) = beta^2+n*psi-n*psi*exp(-2*lambda*Pi/(n*omega0)), (2, 2) = 2*Zeta*beta+lambda, (2, 3) = n*psi*v*exp(-2*lambda*Pi/(n*omega0))-n*psi*v, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = lambda, (3, 4) = -1, (4, 1) = n-n*exp(-2*lambda*Pi/(n*omega0)), (4, 2) = 0, (4, 3) = -n*v+1+n*v*exp(-2*lambda*Pi/(n*omega0)), (4, 4) = 2*kappa+lambda}), Vector(4, {(1) = 0, (2) = 0, (3) = 0, (4) = 0})

(6)
> 

> 

right_vector := Matrix(4, 1, [r[1], r[2], r[3], r[4]])

right_vector := Matrix(4, 1, {(1, 1) = r[1], (2, 1) = r[2], (3, 1) = r[3], (4, 1) = r[4]})

(7)
> 

junk := MatrixVectorMultiply(subs(lambda = I*omega, A), right_vector)

junk := Matrix(4, 1, {(1, 1) = I*omega*r[1]-r[2], (2, 1) = (beta^2+n*psi-n*psi*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(2*Zeta*beta+I*omega)*r[2]+(n*psi*v*exp(-(2*I)*omega*Pi/(n*omega0))-n*psi*v)*r[3], (3, 1) = I*omega*r[3]-r[4], (4, 1) = (n-n*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(-n*v+1+n*v*exp(-(2*I)*omega*Pi/(n*omega0)))*r[3]+(2*kappa+I*omega)*r[4]})

(8)
> 

junk(1)

I*omega*r[1]-r[2]

(9)
> 

for k to 4 do eqnn[k] := junk(k) end do

I*omega*r[1]-r[2]

 

(beta^2+n*psi-n*psi*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(2*zeta*beta+I*omega)*r[2]+(n*psi*v*exp(-(2*I)*omega*Pi/(n*omega0))-n*psi*v)*r[3]

 

I*omega*r[3]-r[4]

 

(n-n*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(1-n*v+n*v*exp(-(2*I)*omega*Pi/(n*omega0)))*r[3]+(2*kappa+I*omega)*r[4]

(10)
> 

solve({seq(eqnn[k], k = 1 .. 4)}, {seq(r[k], k = 1 .. 4)})

{r[1] = 0, r[2] = 0, r[3] = 0, r[4] = 0}

(11)
> 

``

> 

``

> 

``

 

Download question4.mw

↧
Search
Viewing all articles
Browse latest Browse all 1089

Trending Articles

Practice Sheet of Right form of verbs for HSC Students

September 22, 2019, 11:40 pm

Download: FK ft Shenky – Nakuyewa ”Prod by: Shenky”

February 16, 2017, 4:24 pm

How to win at Markstrat (Markstrat Tips and Tricks) – Vodites

January 5, 2014, 10:34 pm

Ominde Commission Report and Recommendations – Ominde Report of 1964

March 16, 2015, 5:14 am

Bureau of Internal Revenue: Regional Offices (Directory)

January 9, 2014, 11:06 pm

GO 53 on Enhancement of Ex-gratia upto 5 Lakhs Toddy Tappers in Telangana

March 26, 2017, 11:23 pm

Cakewalk CA-2A Leveling Amplifier v2.0.1.97 WiN, v2.0.1.96 OSX Incl Keygen

October 17, 2016, 7:20 am

Mp3 Download: Mdu - Kunjenjenjena

December 7, 2017, 8:16 am

How the kill the job , when DTP request running for long hours.

July 26, 2013, 2:41 am

Microsoft Intune から展開しているアプリのアップデートについて

October 17, 2016, 4:11 am

18-year-old girl was beaten for half an hour by two Northampton men in 'an...

September 1, 2017, 10:00 pm

Car crash in Dunton Bassett leaves driver in critical condition

October 7, 2014, 7:51 am

Macky 2, Two Others In Road Accident

March 29, 2015, 5:34 am

Application log 00000000000000089514: Could not convert queue DLVST90CLNT

May 14, 2015, 11:27 pm

Detroit mafia: D’Anna Brothers agree to plea deal

April 21, 2016, 6:56 am

Delivery block field greyed out using VA02

January 26, 2016, 2:52 pm

Muloraki Au

June 22, 2016, 1:44 am

【個人撮影】スマホのプライベート映像♪「中に出さないで///」カラオケ屋での生ハメ撮りが流出ｗ【リベンジポルノ】＠PornHub

October 12, 2017, 2:23 pm

BREAKING NEWS: Diamond Platnumz Is Reported Dead After Ghastly Car Accident

February 9, 2018, 4:56 am

FIAT 500 B0111 B0112

July 5, 2018, 10:31 am
Search