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pik1432

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These are questions asked by pik1432

RE: how to apply product to sum identiti...

pik1432 245 Maple
simplification trig identity
September 01 2020
3 9

Dear all, 

Would you tell me a way to apply the identity relationship in Maple, to rewrite 'subexp' below to 'subexp2'?


 

> 

restart;
> 

subexp := M__a*sin(omega*t + alpha)*I__a*sin(omega*t + phi);

M__a*sin(omega*t+alpha)*I__a*sin(omega*t+phi)

 (1)
> 

subexp2 := M__a * I__a * (-1/2*(cos(2*omega*t + alpha + phi)-cos(alpha - phi)));

M__a*I__a*(-(1/2)*cos(2*omega*t+alpha+phi)+(1/2)*cos(alpha-phi))

 (2)
> 

is(subexp = subexp2);

true

 (3)
> 

 


 

Download Q20200901.mw

Re: Difference between Maple and MATLAB...

pik1432 245 Maple
matlab dynamicsystems
August 26 2020
2 3

Dear All, 

When I checked the dynamic responses of second-order systems, I saw this:

While MATLAB step response shows a smooth curve (the blue one), Maple came up with wiggles (the blue one).

What might have worked on Maple's side to make the curve wiggling?

The Maple worksheet as well as MATLAB M script are attached. The MATLAB M script extension (.m) is not allowed, therefore it was modified to '.txt'. 

Sallen_Key.mw

SallenKey_check.txt

RE: How to reweite an expression...

pik1432 245 Maple
factorization simplification
August 17 2020
2 2

Dear all, 

Would you allow me to ask a question?

What would be a way to re-write the 'eq2' in the following worksheet as 'eq_given'? The check, 'is...'. shows that two expressions are the same. 


 

> 

restart;eq1:= (-k*I + 2*I + m)*sqrt(3) - 3*I*m - 3*k;

(-I*k+2*I+m)*3^(1/2)-(3*I)*m-3*k

 (1)
> 

eq2:=eq1 / 2;

(1/2)*(-I*k+2*I+m)*3^(1/2)-((3/2)*I)*m-(3/2)*k

 (2)
> 

eq_given:= (-sqrt(3)*I/2 - 3/2)*(k + I*m) + sqrt(3)*I;

(-((1/2)*I)*3^(1/2)-3/2)*(k+I*m)+I*3^(1/2)

 (3)
> 

is(eq_given - eq2 = 0);

true

 (4)
> 

 


Thank you, 

Download Q20200817.mw

RE: replacing all subexpressions...

pik1432 245 Maple
substitution
August 12 2020
1 1

Dear All, 

When I tried to replace all occurrences of an expression (two occurrences in total), only one of them (the last one with 'R__arm/2' coefficient) was replaced. I wonder if there is a way to make sure that all the occurrences are replaced by the intended substitute. 


 

> 

restart;
> 

with(Student[LinearAlgebra]):
> 

eq4:= v__a(t) = (v__an(t)-v__ap(t))/2 - L__arm/2*diff([i__ap(t)-i__an(t)], t) - R__arm/2*(i__ap(t)-i__an(t));

v__a(t) = (1/2)*v__an(t)-(1/2)*v__ap(t)-(1/2)*L__arm*[diff(i__ap(t), t)-(diff(i__an(t), t))]-(1/2)*R__arm*(i__ap(t)-i__an(t))

 (1)
> 

eq4_2:= subs([i__ap(t)-i__an(t) = i__a(t)], eq4);

v__a(t) = (1/2)*v__an(t)-(1/2)*v__ap(t)-(1/2)*L__arm*[diff(i__ap(t), t)-(diff(i__an(t), t))]-(1/2)*R__arm*i__a(t)

 (2)
> 

 


 

Download Maximum_Modulation_Index_for_MMC_with_CCC.mw

RE: 'fsolve' unable to solve once 'conju...

pik1432 245 Maple
fsolve
August 10 2020
1 12

Hello there, 

Here is a set of non-linear equations:

 

> 

restart;
> 

with(LinearAlgebra):
> 

TrainLoad := -10*10^6*(cos(convert(40*degrees, radians))+I*sin(convert(40*degrees, radians)));

-10000000*cos((2/9)*Pi)-(10000000*I)*sin((2/9)*Pi)

 (1)
> 

 

> 

evalf(TrainLoad, 7);

-7660444.-6427876.*I

 (2)
> 

f1n2 := (0.03 + I*0.1515)*Ix[c1] - (0.03 + I*0.1515)*Ix[c2] + 2 * V[at1] - 55*10^3 = 0;

(0.3e-1+.1515*I)*Ix[c1]+(-0.3e-1-.1515*I)*Ix[c2]+2*V[at1]-55000 = 0

 (3)
> 

f3n4 := (1.6 + I*6.24)*Ix[c1] + (1.12 + I*2.64)*Ix[c2] + V[t] - V[at1] = 0;

(1.6+6.24*I)*Ix[c1]+(1.12+2.64*I)*Ix[c2]+V[t]-V[at1] = 0

 (4)
> 

f5n6 := (1.36 + I*4.44)*Ix[c2] + V[at2] - V[t] = 0;

(1.36+4.44*I)*Ix[c2]+V[at2]-V[t] = 0

 (5)
> 

f7n8 := (-1.12 - I*2.64)*Ix[c1] + (-3.92 - I*12.00)*Ix[c2] + V[at2] - V[at1] = 0;

(-1.12-2.64*I)*Ix[c1]+(-3.92-12.00*I)*Ix[c2]+V[at2]-V[at1] = 0

 (6)
> 

f9n10 := V[t] * (Ix[c1] - Ix[c2]) + TrainLoad = 0;

V[t]*(Ix[c1]-Ix[c2])-10000000*cos((2/9)*Pi)-(10000000*I)*sin((2/9)*Pi) = 0

 (7)
> 

polynomials := {f1n2, f3n4, f5n6, f7n8, f9n10};

{(1.36+4.44*I)*Ix[c2]+V[at2]-V[t] = 0, V[t]*(Ix[c1]-Ix[c2])-10000000*cos((2/9)*Pi)-(10000000*I)*sin((2/9)*Pi) = 0, (-1.12-2.64*I)*Ix[c1]+(-3.92-12.00*I)*Ix[c2]+V[at2]-V[at1] = 0, (0.3e-1+.1515*I)*Ix[c1]+(-0.3e-1-.1515*I)*Ix[c2]+2*V[at1]-55000 = 0, (1.6+6.24*I)*Ix[c1]+(1.12+2.64*I)*Ix[c2]+V[t]-V[at1] = 0}

 (8)
> 

variables := {Ix[c1], Ix[c2], V[at1], V[at2], V[t]};

{Ix[c1], Ix[c2], V[at1], V[at2], V[t]}

 (9)
> 

fsolve(polynomials, variables, complex);

{Ix[c1] = 955.2297105-5281.491898*I, Ix[c2] = -505.0156845+2424.830843*I, V[at1] = 26894.34238+4.981252431*I, V[at2] = 10829.70666+56.66545127*I, V[t] = -623.3636109+1112.165758*I}

 (10)
> 

 

> 

 


The 'fsolve()' command was able to come up with a solution. 

Then, when 'f9n10 := V[t] * (Ix[c1] - Ix[c2]) + TrainLoad = 0;' becomes 'f9n10 := V[t] * conjugate(Ix[c1] - Ix[c2]) + TrainLoad = 0;', 

the command ('fsolve()') refused to produce a solution. 

Would you tell me how to make the 'fsolve()' command work with the 'conjugate()' operator?

Thank you, 

In Kwon Park


 

 

Download no_conjugate.mw

 

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