faizfrhn

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These are replies submitted by faizfrhn

@acer hi acer sorry for the repeated question. I will not do it again.

I don't know that I can you square bracket insted of round bracket, I will change it in my future work.

I meant to write 90 degree, so I think from now on I will need to use it in terms of pi.

I made an unintentional mistake at the last part, it should be sin((theta + 90 + delta - beta + phi)).

Thank you for your help and assitance.

Kind regards

Faiz Farhan

@Carl Love Hi Carl, sorry for the mistakes, and thanks for your participation!

Let me rearrange the question of this differentiation, so I have the equation as follow

eq3 := P = 1/2*gamma*H^2*[cos(theta - beta)*cos(theta - alpha)*sin(beta - phi)/(cos(theta)^2*sin(beta - alpha)*sin(((beta + 90 + delta) - beta) + phi))]

 

And according to the paper I read, to get the critical value of beta for maximum value of P, I need to make differentiation to first derivative where dP/d(beta) = 0.

Note that in this case only beta is the only variables, and other coefficients are constant.

Then I should substitute back value of beta to equation above and the paper shows that i should get equation below.

P = 1/2*K*gamma*H^2

 

where K is equal to

K = cos(phi - theta)^2/(cos(theta)^2*cos(theta + delta)*(1 + sqrt(sin(delta + phi)*sin(phi - alpha)/(cos(theta + delta)*cos(theta - alpha))))^2)

Hope you can help me with this. It's good enough if I can learn how to perform differentiate with respect to variable.

Thank you again :)

 

Regards

Faiz Farhan

@Carl Love thank you for your solution.

May I know why you use 2= H^2*.. in front of the command?

 

@Kitonum 


 

eq1 := `S__2 ` = (W__1+W__2)*sin(alpha-phi)/sin(beta+delta+phi-alpha)-S__1

`S__2 ` = -(W__1+W__2)*sin(alpha-phi)/sin(-beta-delta-phi+alpha)-S__1

(1)

eq2 := W__1+W__2 = (1/2)*gamma*H^2*sin(beta-alpha)*sin(beta-epsilon)/(sin^2*beta*sin(alpha-epsilon))-(1/2*(gamma-psi))*h^2*sin(beta-alpha)/((sin*beta*sin)*alpha)

W__1+W__2 = -(1/2)*gamma*H^2*sin(-beta+alpha)*sin(beta-varepsilon)/(sin^2*beta*sin(alpha-varepsilon))+(1/2)*(gamma-psi)*h^2*sin(-beta+alpha)/(sin^2*beta*alpha)

(2)

````

``

eq3 := algsubs(eq2, eq1)

`S__2 ` = (1/2)*sin(alpha-phi)*sin(-beta+alpha)*(gamma*H^2*sin(beta-varepsilon)*alpha-h^2*sin(alpha-varepsilon)*gamma+h^2*sin(alpha-varepsilon)*psi)/(sin(-beta-delta-phi+alpha)*sin^2*beta*sin(alpha-varepsilon)*alpha)-S__1

(3)

``

``

Is there any way that we let Maple simplify above expression (eq3) to a much simpler form of solution below?

 

the solution provided is as follow, `S__2 ` = (1/2)*gamma(1-((gamma-psi)/gamma)(h/H)^2)*K*H^2-S__1

`S__2 ` = (1/2)*gamma(1-(gamma(h/H)-psi(h/H))^2/gamma(h/H)^2)*K*H^2-S__1

(4)

 

 

where K is,

"K =(((sin(beta+phi))/(sin beta))/(sqrt(sin(beta+delta)+(sqrt(sin(phi+delta)*sin(phi - epsilon)))/(sin(beta-epsilon))))^(2)"

Error, unable to match delimiters

"K =((((sin(beta+phi))/(sin beta))/(sqrt(sin(beta+delta)+(sqrt(sin(phi+delta)*sin(phi - epsilon)))/(sin(beta-epsilon)))))^2"

 

and

gamma(1-((gamma-psi)/gamma)(h/H)^2)= M

gamma(1-(gamma(h/H)-psi(h/H))^2/gamma(h/H)^2)

(5)

``

so that, `S__2 ` = (1/2)*M*K*H^2-S__1


 

Download Worksheet.mwWorksheet.mw

Thank you for your help! I really appreciate that.

I succesfully found the solution based on the way you taught.

Now I am stuck at some more complicated expressions, equation and variable.

I really hope you can help me to take a look into this and give me some idea how to get to the solution.

Thank you very much.

Kind regards,

Faiz Farhan

@nm Thank you for your help! I really appreciate that.

I succesfully found the solution based on the way you taught.

Now I am stuck at some more complicated expressions, equation and variable.

I have compiled it into one worksheet and I really hope you can help me to take a look into this and give me some idea how to get to the solution.

Thank you very much.

Kind regards,

 

eq1 := `S__2 ` = (W__1+W__2)*sin(alpha-phi)/sin(beta+delta+phi-alpha)-S__1

`S__2 ` = -(W__1+W__2)*sin(alpha-phi)/sin(-beta-delta-phi+alpha)-S__1

(1)

eq2 := W__1+W__2 = (1/2)*gamma*H^2*sin(beta-alpha)*sin(beta-epsilon)/(sin^2*beta*sin(alpha-epsilon))-(1/2*(gamma-psi))*h^2*sin(beta-alpha)/((sin*beta*sin)*alpha)

W__1+W__2 = -(1/2)*gamma*H^2*sin(-beta+alpha)*sin(beta-varepsilon)/(sin^2*beta*sin(alpha-varepsilon))+(1/2)*(gamma-psi)*h^2*sin(-beta+alpha)/(sin^2*beta*alpha)

(2)

````

``

eq3 := algsubs(eq2, eq1)

`S__2 ` = (1/2)*sin(alpha-phi)*sin(-beta+alpha)*(gamma*H^2*sin(beta-varepsilon)*alpha-h^2*sin(alpha-varepsilon)*gamma+h^2*sin(alpha-varepsilon)*psi)/(sin(-beta-delta-phi+alpha)*sin^2*beta*sin(alpha-varepsilon)*alpha)-S__1

(3)

``

``

Is there any way that we let Maple simplify above expression (eq3) to a much simpler form of solution below?

 

the solution provided is as follow, `S__2 ` = (1/2)*gamma(1-((gamma-psi)/gamma)(h/H)^2)*K*H^2-S__1

`S__2 ` = (1/2)*gamma(1-(gamma(h/H)-psi(h/H))^2/gamma(h/H)^2)*K*H^2-S__1

(4)

 

 

where K is,

"K =(((sin(beta+phi))/(sin beta))/(sqrt(sin(beta+delta)+(sqrt(sin(phi+delta)*sin(phi - epsilon)))/(sin(beta-epsilon))))^(2)"

Error, unable to match delimiters

"K =((((sin(beta+phi))/(sin beta))/(sqrt(sin(beta+delta)+(sqrt(sin(phi+delta)*sin(phi - epsilon)))/(sin(beta-epsilon)))))^2"

 

and

gamma(1-((gamma-psi)/gamma)(h/H)^2)= M

gamma(1-(gamma(h/H)-psi(h/H))^2/gamma(h/H)^2)

(5)

``

so that, `S__2 ` = (1/2)*M*K*H^2-S__1


 

Download Worksheet.mwWorksheet.mw

Faiz Farhan

 

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