pik1432

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These are questions asked by pik1432

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

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

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

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

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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