Items tagged with equation

hi.

how i can solve two equation with respect to parameter sigma1

SOLL.mw

restart; pprime11 := -16395.36603*q1+5.811117425*q1*sigma1^2+3526.724044*p1-1.250000000*p1*sigma1^2+4.999870968*10^11*p1^3+4.999870970*10^11*p1*q1^2+7.967307034*10^14*p1^2*q1+4.999870966*10^12*sigma1*p1^2*q1-2.655769012*10^14*q1^3+4.999870968*10^12*sigma1*q1^3-17633.62022*q1*sigma1+6.250000000*q1*sigma1^3

qprime11 := 2.655769012*10^14*p1^3-7.967307034*10^14*p1*q1^2+4.999870970*10^11*p1^2*q1-4.999870968*10^12*sigma1*p1^3-4.999870966*10^12*p1*sigma1*q1^2+3526.724044*q1-1.250000000*q1*sigma1^2+16395.36603*p1-5.811117425*p1*sigma1^2+4.999870968*10^11*q1^3+17633.62022*p1*sigma1-6.250000000*p1*sigma1^3:

-50 < sigma1 and sigma1 < 50:

sigma1 <> 53.11665685, -53.11665685:

SOLL := solve({pprime11, qprime11}, real)

Warning,  computation interrupted

 

``

 

Download SOLL.mw

 

With the following equation

eqn:=y=1/2+(1/2)*erf((1/2)*sqrt(2)*(x-mu)/sigma)-exp(-lambda*(x-mu)+(1/2)*lambda^2*sigma^2+ln(1/2-(1/2)*erf((1/2)*sqrt(2)*(lambda^2*sigma^2-lambda*(x-mu))/(lambda*sigma))));

and with

x:=solve(eqn,x) assuming sigma > 0, lambda > 0;

I got the following solution

x := -(1/2)*(-lambda^2*sigma^2-2*lambda*mu+2*RootOf(-exp(_Z)*erf((1/4)*sqrt(2)*(lambda^2*sigma^2+2*_Z)/(lambda*sigma))+exp(_Z)+erf((1/4)*sqrt(2)*(-lambda^2*sigma^2+2*_Z)/(lambda*sigma))+2*y-1))/lambda;

In order to get rid of RootOf I gave the command:

allvalues(%);

However, RootOf did not disappear. How should I proceed? 

 

Hello,

 

I am unable to use subs() command when using subscript : I'd like to replace YP__1 with dGx in the equation :

"Eq:= YP__1 = Y__2" (Eq:= YP1=Y2)

 

 so I have tried : subs({YP__1=dGx},Eq)

 

But it doesn't work... It give me : YP__1 = Y__2 and I would like to have dGx = Y__2

 

I have tried also with subs({YP[1]=dGx},Eq) but doesn't work too.

 

If I am not using subscript, for exemple : Eq:= YP1 = Y2

 

And do : subs({YP1=dGx},Eq)

 

That works great...

 

But I must use subscript __ because Eq is a result from ODEtools (convertsys).

 

Can you help me please ?

 

Thanks you very much.

 

Regards.

When I was editing the head of the question (? instead of .), its body disappeared. Please, insert it again.

Regard,

Markiyan Hirnyk

If L is a list [a,c,b,d,f,e]

S is a list [b,c,f,e]

I want to use the permutation opf S to rearrange L [b,c,f,e,a,d]

In my case a,b,c,d,e,f are equations.

I have checked many Maple pages and I found nowhere the answer to this question.

EQ:= s^2-4*s+1=3;

I need to print the following statement:

The Equation Is: EQ

I need the equation to appear where EQ is.

Thank you guys!

I appreciate it.

 

 

 

Here is a code

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/EQ.mw .

Download EQ.mw

A fragment of code

for b in extra_bcs do try print(b = 10^(-2)); res[b] := dsolve(dsys4 union {b = 10^(-2)}, numeric, initmesh = 2024, output = listprocedure, approxsoln = [omega2 = 0.1e-2, s(x) = cosh(upsilon*x)-cos(upsilon*x)-(cosh(upsilon)+cos(upsilon))*(sinh(upsilon*x)-sin(upsilon*x))/(sinh(upsilon)+sin(upsilon)), g(x) = sin(((2*n+1)*(1/2))*Pi)], abserr = 0.1e-1) catch: print(lasterror) end try end do; indx := indices(res, nolist); nops([indx]); res[indx[i]]; seq(subs(res[indx[i]](1), omega2(1)), i = 1 .. nops([indx]))

Hello,

I would like to simplify a trigonometric equation that I obtain with a vectorial closure (in mechanics)

Here the equation that I would like to simplify 

eq_liaison :=(-sin(p(t)+g(t))*cos(a(t))-sin(b(t))*sin(a(t))*cos(p(t)+g(t)))*l2[1]+((-sin(p(t)+g(t))*cos(a(t))-sin(b(t))*sin(a(t))*cos(p(t)+g(t)))*cos(th(t))+(-cos(p(t)+g(t))*cos(a(t))+sin(a(t))*sin(b(t))*sin(p(t)+g(t)))*sin(th(t)))*l3[1] = 0

Do you have ideas so as to simplify again this expression ?

This expression can still be simplified. You can find here the result expected :

I find surprising that I have so many difficulties to make trigonometric simplications with the trigonometric functions.

Thank you for your help

PS : Sorry for duplicating posts. As I didn't receive any answer, I have tried to simplified my post to isolate the difficulty.

I am using maple 13 to get the resualt of the einstein filed equations

 

with(tensor)

...

Estn := Einstein(metric, RICCI, RS);

displayGR(Einstein, Estn);

 

How can i put the resualt on a array element, so i can use it later on?

 

 

Hello,

I would like to determine the position jacobian matrix from a set of constraint equations.

Here my constraint equations :

eq1:=l1*cos(theta(t))+l2*sin(beta(t))-x(t)=0
eq2:=l1*sin(theta(t))-l2*cos(beta(t))=0

The jacobian matrix that I would like to determine is :

 

Can you help me to make a general procedure to calculate a jacobian position matrix from a set of constraint equations ?

Thank you for your help

 

Hello,

I would like to simplify this following trigonometric expression :

Code:
eq_liaison:= x0(t)-sin(alpha0(t))*sin(gamma0(t))*sin(beta0(t))*xb[1]+sin(alpha0(t))*sin(beta0(t))*cos(gamma0(t))*zb[1]+sin(alpha0(t))*cos(beta0(t))*yb[1]+cos(alpha0(t))*sin(gamma0(t))*zb[1]+cos(alpha0(t))*cos(gamma0(t))*xb[1]+l2[1]*(sin(psi[1](t))*sin(alpha0(t))*sin(gamma0(t))*sin(beta0(t))-cos(psi[1](t))*sin(alpha0(t))*sin(beta0(t))*cos(gamma0(t))-sin(psi[1](t))*cos(alpha0(t))*cos(gamma0(t))-cos(psi[1](t))*cos(alpha0(t))*sin(gamma0(t)))+l3[1]*(sin(theta[1](t))*sin(psi[1](t))*sin(alpha0(t))*sin(beta0(t))*cos(gamma0(t))+sin(theta[1](t))*cos(psi[1](t))*sin(alpha0(t))*sin(gamma0(t))*sin(beta0(t))+cos(theta[1](t))*sin(psi[1](t))*sin(alpha0(t))*sin(gamma0(t))*sin(beta0(t))-cos(theta[1](t))*cos(psi[1](t))*sin(alpha0(t))*sin(beta0(t))*cos(gamma0(t))+sin(theta[1](t))*sin(psi[1](t))*cos(alpha0(t))*sin(gamma0(t))-sin(theta[1](t))*cos(psi[1](t))*cos(alpha0(t))*cos(gamma0(t))-cos(theta[1](t))*sin(psi[1](t))*cos(alpha0(t))*cos(gamma0(t))-cos(theta[1](t))*cos(psi[1](t))*cos(alpha0(t))*sin(gamma0(t)))-xp[1](t) = 0

I would like to make groups like : cos(a)cos(b) - sin(a)sin(b)=cos(a+b)  but keepind the maximum of expression products

On the following example (2 equations below), the function combine(expr,trig) works well 

Code:
eq_liaison[1] := cos(gamma(t))*r+(cos(gamma(t))*cos(psi(t))-sin(gamma(t))*sin(psi(t)))*l-x(t) = 0 
eq_liaison[2] := sin(gamma(t))*r+(sin(gamma(t))*cos(psi(t))+cos(gamma(t))*sin(psi(t)))*l = 0



But, I would like maple do only the first simplifications in order to the maximum of expression products. The function combine(expr,trig) goes too far in the first equation and I obtain only expression sums. 

Do you have ideas to simplify the first trigonometric equations
- with groups like : cos(a)cos(b) - sin(a)sin(b)=cos(a+b)
- and keeping products of expressions ?

Thank you for your help

A := Vector([1, 2, 3])

solve(2*A = 5+x, {x})

 

can anyone help me why i am having proble to solve for x?

Thanks

Hi!

 

For some reason my three equation with three unknowns won't be solved. Anyone who can help? I tried the following:

Really appreciate anyone who can help me out!

 

Hi, does anyone know how to choose the variables that populate the DAE Variables box when you use "equation extraction"?

I want the result to be in terms of the voltage source and the voltage drop across the capacitor for a RLC circuit.  I want to be able to choose the input-output variables for the final equation.

 

 

Hi everyone...!

Can somebody tell me how to express this equation in Maple? 

xij <= zkl ; ∀ i ∈ I: S(i)=k, ∀ j ∈ B: R(j)=l; 

Currently I'm dealing with containerization problem and have 4 indexes in the constraints (namely: i for item, j for container, k for shipment, l for route, S for Set of Shipment, and R for Set of Route) while x and z are binary variables. What I want to express is: (for example), item 1,2,3 are in shipment 1, item 4,5 are in shipment 2, etc etc. SO, if i = 1,2,3 then the value of k will be 1. If i = 4,5 then the value of k will be 2, etc. Same thing goes to j and l, (for example) if j = 1,2 then the value of l will be 1, etc etc. Further depcition is more or less like this:

S(i) = k

S(1) = 1

S(2) = 1

S(3) = 1

S(4) = 2

S(5) = 2

 

Thank you very much for the help.

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