Items tagged with simplification

I'm creating a randomly generated question bank that generates the following STYLE or problem:

12x-4y2
3x6y-5

I'm currently trying to use the answer type "formula without simplification," as I'd like to avoid the students putting the questions in as the answer, and this has been driving me crazy for hours now.

I have tried the "maple" function to simplify. E.g.:

$ANS = maple("( $C1*( $V1^$A1 )*( $V2^$B1 ) ) / ( $C2*( $V1^$A2 )*( $V2^$B2 ) )");

But it always throws an error.

I have simply done the math in the algorithm section, so you end up with an answer variable like this:

$ANS = -4.0*(((z)^2.0)/(5.0*((p)^9.0)))

However, it will still count all answers submitted as incorrect.

Any help would be GREATLY appreciated =/.

 

 

Variable name clarification
I have $C1 and $C2, which are the constants of the numerator and denominator, respectively ("12" and "3" in the example).
I have $V1 and $V2 which are the first and second variable, respectively, (in the example, "x" and "y").
I have $A1 and $A2, which are the exponents for the variable $V1 in the numerator and denominator, respectively.
I have $B1 and $B2, which are the exponents for the variable $V2 in the numerator and denominator, respectively.

All these generate from some interesting conditions to create the problems I want (no variables named i, e, or o, for example,) but all properly initialize.

HI everyone,

As can be seen from the attached file, the first three equations of Eq. (5) will render some of the other equations (and other terms) redundant. How can I obtain a simplified system automatically?

Thanks.

Pdesample.mw

Dear all:

I have used the "diff" command in Maple to help me derive a huge and very long function, and now I want to convert this huge expression from Maple to Matlab format, for example, into a Matlab .m file. The format of this expression in Maple is very different from Matlab.

So could you help me with this problem?

Thank you all.

How do I convince MAPLE to simplify this Euclidean norm? > (D[1](P))(rho, theta, phi); Vector[column](%id = 230612588) > Norm(%, 2); / 2 2 2\ \|cos(phi) sin(theta)| + |sin(phi) sin(theta)| + |cos(theta)| /^ (1/2) > simplify(%, trig); / 2 2 2\ \|cos(phi) sin(theta)| + |sin(phi) sin(theta)| + |cos(theta)| /^ (1/2)

Hi folks,

I've come across this project which involves large algebraic expressions and I need to be able to simplify it using Maples in-built features, but with no succes.

The problem involves trig-functions. For instance I have several expressions involving:

       cos(v)*sin(w)-cos(w)*sin(v)       which I know equals     -sin(v-w)

but even if I use simplify, trig, size and so on it won't apply the above identity. Btw there are several other identities that aren't applied either.

Is there any way to "force" the above identity into consideration??

how i can simplify

(f(x[n])/Df(x[n]));
in code

restart;
taylor(f(x), x = gamma, 8);
f(x[n]) := subs([x-gamma = e[n], f(gamma) = 0, seq(((D@@k)(f))(gamma) = factorial(k)*c[k]*(D(f))(gamma), k = 1 .. 1000)], %);

1 2
f(gamma) + D(f)(gamma) (x - gamma) + - @@(D, 2)(f)(gamma) (x - gamma)
2

1 3 1 4
+ - @@(D, 3)(f)(gamma) (x - gamma) + -- @@(D, 4)(f)(gamma) (x - gamma)
6 24

1 5 1 6
+ --- @@(D, 5)(f)(gamma) (x - gamma) + --- @@(D, 6)(f)(gamma) (x - gamma)
120 720

1 7 / 8\
+ ---- @@(D, 7)(f)(gamma) (x - gamma) + O\(x - gamma) /
5040
2 3
c[1] D(f)(gamma) e[n] + c[2] D(f)(gamma) e[n] + c[3] D(f)(gamma) e[n]

4 5 6
+ c[4] D(f)(gamma) e[n] + c[5] D(f)(gamma) e[n] + c[6] D(f)(gamma) e[n]

7 / 8\
+ c[7] D(f)(gamma) e[n] + O\e[n] /

taylor(D(f)(x), x = gamma, 8);
Df(x[n]) := subs([x-gamma = e[n], f(gamma) = 0, seq(((D@@k)(f))(gamma) = factorial(k)*c[k]*(D(f))(gamma), k = 2 .. 1000)], %);

D(f)(gamma) + @@(D, 2)(f)(gamma) (x - gamma)

1 2 1 3
+ - @@(D, 3)(f)(gamma) (x - gamma) + - @@(D, 4)(f)(gamma) (x - gamma)
2 6

1 4 1 5
+ -- @@(D, 5)(f)(gamma) (x - gamma) + --- @@(D, 6)(f)(gamma) (x - gamma)
24 120

1 6
+ --- @@(D, 7)(f)(gamma) (x - gamma)
720

1 7 / 8\
+ ---- @@(D, 8)(f)(gamma) (x - gamma) + O\(x - gamma) /
5040
2
D(f)(gamma) + 2 c[2] D(f)(gamma) e[n] + 3 c[3] D(f)(gamma) e[n]

3 4
+ 4 c[4] D(f)(gamma) e[n] + 5 c[5] D(f)(gamma) e[n]

5 6
+ 6 c[6] D(f)(gamma) e[n] + 7 c[7] D(f)(gamma) e[n]

7 / 8\
+ 8 c[8] D(f)(gamma) e[n] + O\e[n] /

(f(x[n])/Df(x[n]));
this last term did not use f(x[n]) value from above to solve it. plxx help if any one can solve it...

Hello,

In the context of solving mechanical constraint equations, I often need to simplify trigonometric equation. In mathematica, the FullSimplify function makes the simplification I need. But, i'm using Maple for a long time and I would rather contnue my calculation with Mathematica.

May you see if so can help me to simplify this equation ?

Here the equation I would like to simplify with Maple :

TrigonometricEquation.mw

Here the result obtained with mathematica

résultatMma.pdf

Thanks a lot for your help

Hello there,

 

Suppose I have a parametric experssion like   P(ε)=1+ε+ε23 where ε is very small. How can I get P(ε)≈1+ε or P(ε)≈1+ε+ε2

 

Thanks

Below I try to use units for a simple expression, where "m" and "mm" is added on Windows using Ctrl-Shift-U.

Why does the value with unit "1 [[m]]" not show as "1 m" in (1), but simply as "m" ?

Why does the addition not result in "2 m" ?

At least I had expected the addition to be made when using "evalf()".

 

Sorry for boring you my friends. I am haunted by a problem of how to omit the undesired term.

For example, in the following equation, the a(t) , b(t), c(t), u(t), v(t), w(t), psi(t), phi(t), theta(t), varsigma(t), tau(t) and upsilon(t) and their first and second direvative to time t are considered as first order small variables. How could I omit the term greater than second order of small variables?

If we omit the undesired by hand, the omitted equation takes the form of:

R^2*rho*h*(diff(w(t), t, t))*Pi+R^2*rho*h*(diff(c(t), t, t))*Pi = 0;

The original equation is given as: 

-R^2*rho*h*cos(Omega*t)*(diff(tau(t), t, t))*a(t)*Pi+tau(t)*R^2*rho*h*(diff(tau(t), t))^2*a(t)*cos(Omega*t)*Pi-tau(t)*R^2*rho*h*(diff(tau(t), t))^2*b(t)*sin(Omega*t)*Pi+tau(t)*a(t)*Pi*cos(Omega*t)*(diff(varsigma(t), t))^2*R^2*h*rho+tau(t)*R^2*rho*h*a(t)*Omega^2*cos(Omega*t)*Pi-tau(t)*sin(Omega*t)*Pi*(diff(varsigma(t), t))^2*b(t)*R^2*h*rho-tau(t)*R^2*rho*h*b(t)*Omega^2*sin(Omega*t)*Pi+2*tau(t)*R^2*rho*h*(diff(a(t), t))*Omega*sin(Omega*t)*Pi+2*tau(t)*R^2*rho*h*(diff(b(t), t))*Omega*cos(Omega*t)*Pi-varsigma(t)*a(t)*sin(Omega*t)*Pi*(diff(varsigma(t), t))^2*R^2*h*rho-varsigma(t)*a(t)*sin(Omega*t)*Pi*Omega^2*R^2*h*rho-varsigma(t)*Pi*cos(Omega*t)*(diff(varsigma(t), t))^2*b(t)*R^2*h*rho-varsigma(t)*Pi*cos(Omega*t)*b(t)*Omega^2*R^2*h*rho-2*varsigma(t)*sin(Omega*t)*Pi*(diff(b(t), t))*Omega*R^2*h*rho+2*varsigma(t)*Pi*cos(Omega*t)*(diff(a(t), t))*Omega*R^2*h*rho+2*a(t)*Pi*cos(Omega*t)*(diff(varsigma(t), t))*Omega*R^2*h*rho-2*sin(Omega*t)*Pi*(diff(varsigma(t), t))*b(t)*Omega*R^2*h*rho+R^2*rho*h*(diff(tau(t), t, t))*sin(Omega*t)*b(t)*Pi+R^2*rho*h*(diff(w(t), t, t))*Pi+R^2*rho*h*(diff(c(t), t, t))*Pi-R^2*rho*h*(diff(tau(t), t))^2*c(t)*Pi+2*varsigma(t)*(diff(tau(t), t))*a(t)*Pi*cos(Omega*t)*(diff(varsigma(t), t))*R^2*h*rho-2*varsigma(t)*(diff(tau(t), t))*sin(Omega*t)*Pi*(diff(varsigma(t), t))*b(t)*R^2*h*rho+a(t)*sin(Omega*t)*Pi*(diff(varsigma(t), t, t))*R^2*h*rho+Pi*cos(Omega*t)*b(t)*(diff(varsigma(t), t, t))*R^2*h*rho-varsigma(t)*Pi*c(t)*(diff(varsigma(t), t, t))*R^2*h*rho-2*tau(t)*R^2*rho*h*(diff(tau(t), t))*(diff(c(t), t))*Pi-2*varsigma(t)*Pi*(diff(varsigma(t), t))*(diff(c(t), t))*R^2*h*rho+2*sin(Omega*t)*Pi*(diff(varsigma(t), t))*(diff(a(t), t))*R^2*h*rho+2*Pi*cos(Omega*t)*(diff(varsigma(t), t))*(diff(b(t), t))*R^2*h*rho-Pi*(diff(varsigma(t), t))^2*c(t)*R^2*h*rho-2*R^2*rho*h*cos(Omega*t)*(diff(tau(t), t))*(diff(a(t), t))*Pi+2*R^2*rho*h*(diff(tau(t), t))*sin(Omega*t)*(diff(b(t), t))*Pi+tau(t)*R^2*rho*h*(diff(b(t), t, t))*sin(Omega*t)*Pi-tau(t)*R^2*rho*h*(diff(a(t), t, t))*cos(Omega*t)*Pi-tau(t)*R^2*rho*h*(diff(tau(t), t, t))*c(t)*Pi+2*R^2*rho*h*Omega*sin(Omega*t)*(diff(tau(t), t))*a(t)*Pi+2*R^2*rho*h*(diff(tau(t), t))*Omega*cos(Omega*t)*b(t)*Pi+varsigma(t)*sin(Omega*t)*Pi*(diff(a(t), t, t))*R^2*h*rho+varsigma(t)*Pi*cos(Omega*t)*(diff(b(t), t, t))*R^2*h*rho = 0;

 

Thank you in advance for taking a look ;)

I'm trying to solve a recurrence relation by generating terms and looking for a pattern.  I've learned that i can't stop 

Maple's autosimplification process and the best I can do is use Parse from the InertForm package.  The hand drawn picture below is what I'm trying to replicate.  I know I can use rsolve but I'm trying to do the steps I would with pencil and paper.

 

Hello,

I have still some difficulties to conduct some specific trigonometric simplications but which are very common in mechanism study.

The equations are in the form :

sin(gamma0(t))*cos(beta0(t)) = -(sin(psi[1](t))*cos(theta[1](t))*cos(gamma[1](t))+sin(psi[1](t))*sin(theta[1](t))*sin(gamma[1](t))-cos(theta[1](t))*cos(psi[1](t))*sin(gamma[1](t))+cos(psi[1](t))*sin(theta[1](t))*cos(gamma[1](t)))*cos(beta[1](t))

I would like to obtain this equation after simplifications :

sin(gamma0(t))*cos(beta0(t)) = cos(beta[1](t))*sin(gamma[1](t)-theta[1](t)-psi[1](t))

I try to make a procedure to automatize the simplification of this kind of trigonometric equation.

Strangely, I noticed that the simplification is done only if there is a minus before the combine function. The simplification works but the result is wrong because i didn't obtain the good sign.

For you information, I try to make these simplifications with MMA and the FullSimplify function of MMA gives directly the expected result that is to say :

I'm sure that it shoud exist a good way to conduct this kind of simplications in Maple.

Can you help me to correct my procedure so to obtain the good result and be enough general, adaptative ? 

Code here and attached in this post :

Initialisation
restart:
with(LinearAlgebra):
with(Student[MultivariateCalculus]):
with(plots):
with(MathML):
with(ListTools):
constants:= ({constants} minus {gamma})[]:
`evalf/gamma`:= proc() end proc:
`evalf/constant/gamma`:= proc() end proc:
unprotect(gamma);
Angular Constraint equations
eq_liaison:=sin(gamma0(t))*cos(beta0(t)) = -(sin(gamma[1](t))*sin(psi[1](t))*sin(theta[1](t))-sin(gamma[1](t))*cos(theta[1](t))*cos(psi[1](t))+cos(gamma[1](t))*sin(psi[1](t))*cos(theta[1](t))+cos(gamma[1](t))*cos(psi[1](t))*sin(theta[1](t)))*cos(beta[1](t)); 
Traitement
TrigoTransform2:= proc(Eq)
local S,S1,tt,pp,Eq2,ListVariables,ListVariablesMod,Subs,size,rhsEq2,lhsEq2;
#Construit une liste à plat#
ListVariables:=indets(Eq, function(identical(t)));
ListVariables:=[op(ListVariables)];
ListVariablesMod:=map(f->cat(op(0,f),_),ListVariables);
Subs:=ListVariables=~ListVariablesMod;
#Variables Changement#
Eq2:=Eq:
print("Equation traitée=",Eq2): 
Eq2:=subs(Subs, Eq2);
print("Equation après subs=",Eq2): 
#Trigonometric transformations#
lhsEq2:=applyrule([
cos(u::anything)*cos(v::anything)-sin(u::anything)*sin(v::anything)=cos(u+v), 
cos(u::anything)*sin (v::anything)+sin(u::anything)*cos(v::anything)=sin(u+v), 
sin(u::anything)*sin(v::anything)-cos(u::anything)*cos(v::anything)=-cos(u+v), 
-sin(v::anything)*cos(u::anything)-sin(u::anything)*cos(v::anything)=-sin(u+v)], simplify(lhs(Eq2), size));
print("Equation lhsEq2 première analyse=",lhsEq2):
rhsEq2:=applyrule([
cos(u::anything)*cos(v::anything)-sin(u::anything)*sin(v::anything)=cos(u+v), 
cos(u::anything)*sin (v::anything)+sin(u::anything)*cos(v::anything)=sin(u+v), 
sin(u::anything)*sin(v::anything)-cos(u::anything)*cos(v::anything)=-cos(u+v), 
-sin(v::anything)*cos(u::anything)-sin(u::anything)*cos(v::anything)=-sin(u+v)], simplify(rhs(Eq2), size));
print("Equation rhsEq2 première analyse=",rhsEq2):
try
lhsEq2:=(trigsubs(2*combine(lhsEq2))[])/2;
print("Equation lhsEq2=",lhsEq2):
catch:
lhsEq2:=lhs(Eq2);
end try;
try
rhsEq2:=(trigsubs(-2*combine(rhsEq2))[])/2;
print("Equation rhsEq2=",rhsEq2):
catch:
rhsEq2:=rhs(Eq2);
end try;
Eq2:= lhsEq2=rhsEq2;
#Variables Changement#
Eq2:=subs(map(t->rhs(t)=lhs(t),Subs),Eq2) 
end proc:
TrigoTransform2(eq_liaison);

TrigoTransformEqAng2_anglais.mws

Thanks a lot for your help.

How can I get maple to express the end result more compact/dense. Like for example in the picture, why can the program not just sum up all the fractions and everything in one number?

 

Hello,

Still on the thematic on simplification of trigonometric expression.

I would like to simplify this equation. Normally, for a mecanical point of view, this equation could be simplified a lot and namely the psi[1](t) and theta[1](t) variables should disappear.

The difference with the former posts is the fact that now each term (for example  2*sin(gamma0(t))*z0(t)*cos(beta0(t))*xb[1]) can regroup 2 terms in factor with the trigonometric part.

eq:=l2[1]^2 = 2*sin(gamma0(t))*z0(t)*cos(beta0(t))*xb[1]-2*sin(gamma0(t))*zp[1](t)*cos(beta0(t))*xb[1]+2*sin(gamma0(t))*y0(t)*sin(alpha0(t))*zb[1]-2*sin(gamma0(t))*yp[1](t)*sin(alpha0(t))*zb[1]+2*sin(gamma0(t))*x0(t)*cos(alpha0(t))*zb[1]-2*sin(gamma0(t))*xp[1](t)*cos(alpha0(t))*zb[1]-2*cos(gamma0(t))*z0(t)*cos(beta0(t))*zb[1]+2*cos(gamma0(t))*zp[1](t)*cos(beta0(t))*zb[1]+2*cos(gamma0(t))*y0(t)*sin(alpha0(t))*xb[1]-2*cos(gamma0(t))*yp[1](t)*sin(alpha0(t))*xb[1]+2*cos(gamma0(t))*x0(t)*cos(alpha0(t))*xb[1]-2*cos(gamma0(t))*xp[1](t)*cos(alpha0(t))*xb[1]+2*y0(t)*cos(alpha0(t))*cos(beta0(t))*yb[1]-2*yp[1](t)*cos(alpha0(t))*cos(beta0(t))*yb[1]-2*x0(t)*sin(alpha0(t))*cos(beta0(t))*yb[1]+2*xp[1](t)*sin(alpha0(t))*cos(beta0(t))*yb[1]-2*sin(psi[1](t))*cos(theta[1](t))*l3[1]*xb[1]+2*sin(psi[1](t))*sin(theta[1](t))*l3[1]*zb[1]-2*cos(theta[1](t))*cos(psi[1](t))*l3[1]*zb[1]-2*cos(psi[1](t))*sin(theta[1](t))*l3[1]*xb[1]-2*sin(gamma0(t))*y0(t)*sin(alpha0(t))*cos(theta[1](t))*cos(psi[1](t))*l3[1]-2*sin(gamma0(t))*yp[1](t)*sin(alpha0(t))*sin(psi[1](t))*sin(theta[1](t))*l3[1]+2*sin(gamma0(t))*yp[1](t)*sin(alpha0(t))*cos(theta[1](t))*cos(psi[1](t))*l3[1]+2*sin(gamma0(t))*x0(t)*cos(alpha0(t))*sin(psi[1](t))*sin(theta[1](t))*l3[1]-2*sin(gamma0(t))*x0(t)*cos(alpha0(t))*cos(theta[1](t))*cos(psi[1](t))*l3[1]-2*sin(gamma0(t))*xp[1](t)*cos(alpha0(t))*sin(psi[1](t))*sin(theta[1](t))*l3[1]+2*sin(gamma0(t))*xp[1](t)*cos(alpha0(t))*cos(theta[1](t))*cos(psi[1](t))*l3[1]-2*cos(gamma0(t))*z0(t)*cos(beta0(t))*sin(psi[1](t))*sin(theta[1](t))*l3[1]+2*cos(gamma0(t))*z0(t)*cos(beta0(t))*cos(theta[1](t))*cos(psi[1](t))*l3[1]+2*cos(gamma0(t))*zp[1](t)*cos(beta0(t))*sin(psi[1](t))*sin(theta[1](t))*l3[1]-2*cos(gamma0(t))*zp[1](t)*cos(beta0(t))*cos(theta[1](t))*cos(psi[1](t))*l3[1]-2*cos(gamma0(t))*y0(t)*sin(alpha0(t))*sin(psi[1](t))*cos(theta[1](t))*l3[1]-2*cos(gamma0(t))*y0(t)*sin(alpha0(t))*cos(psi[1](t))*sin(theta[1](t))*l3[1]+2*cos(gamma0(t))*yp[1](t)*sin(alpha0(t))*sin(psi[1](t))*cos(theta[1](t))*l3[1]+2*cos(gamma0(t))*yp[1](t)*sin(alpha0(t))*cos(psi[1](t))*sin(theta[1](t))*l3[1]-2*cos(gamma0(t))*x0(t)*cos(alpha0(t))*sin(psi[1](t))*cos(theta[1](t))*l3[1]-2*cos(gamma0(t))*x0(t)*cos(alpha0(t))*cos(psi[1](t))*sin(theta[1](t))*l3[1]+2*cos(gamma0(t))*xp[1](t)*cos(alpha0(t))*sin(psi[1](t))*cos(theta[1](t))*l3[1]+2*cos(gamma0(t))*xp[1](t)*cos(alpha0(t))*cos(psi[1](t))*sin(theta[1](t))*l3[1]+yb[1]^2+xb[1]^2+zb[1]^2+l3[1]^2+z0(t)^2+zp[1](t)^2+y0(t)^2+yp[1](t)^2+x0(t)^2+xp[1](t)^2+2*z0(t)*sin(beta0(t))*yb[1]-2*zp[1](t)*sin(beta0(t))*yb[1]-2*z0(t)*zp[1](t)-2*y0(t)*yp[1](t)-2*x0(t)*xp[1](t)-2*sin(gamma0(t))*y0(t)*cos(alpha0(t))*sin(beta0(t))*xb[1]+2*sin(gamma0(t))*yp[1](t)*cos(alpha0(t))*sin(beta0(t))*xb[1]+2*sin(gamma0(t))*x0(t)*sin(alpha0(t))*sin(beta0(t))*xb[1]-2*sin(gamma0(t))*xp[1](t)*sin(alpha0(t))*sin(beta0(t))*xb[1]+2*cos(gamma0(t))*y0(t)*cos(alpha0(t))*sin(beta0(t))*zb[1]-2*cos(gamma0(t))*yp[1](t)*cos(alpha0(t))*sin(beta0(t))*zb[1]-2*cos(gamma0(t))*x0(t)*sin(alpha0(t))*sin(beta0(t))*zb[1]+2*cos(gamma0(t))*xp[1](t)*sin(alpha0(t))*sin(beta0(t))*zb[1]-2*sin(gamma0(t))*z0(t)*cos(beta0(t))*sin(psi[1](t))*cos(theta[1](t))*l3[1]-2*sin(gamma0(t))*z0(t)*cos(beta0(t))*cos(psi[1](t))*sin(theta[1](t))*l3[1]+2*sin(gamma0(t))*zp[1](t)*cos(beta0(t))*sin(psi[1](t))*cos(theta[1](t))*l3[1]+2*sin(gamma0(t))*zp[1](t)*cos(beta0(t))*cos(psi[1](t))*sin(theta[1](t))*l3[1]+2*sin(gamma0(t))*y0(t)*sin(alpha0(t))*sin(psi[1](t))*sin(theta[1](t))*l3[1]+2*sin(gamma0(t))*y0(t)*cos(alpha0(t))*sin(beta0(t))*sin(psi[1](t))*cos(theta[1](t))*l3[1]+2*sin(gamma0(t))*y0(t)*cos(alpha0(t))*sin(beta0(t))*cos(psi[1](t))*sin(theta[1](t))*l3[1]-2*sin(gamma0(t))*yp[1](t)*cos(alpha0(t))*sin(beta0(t))*sin(psi[1](t))*cos(theta[1](t))*l3[1]-2*sin(gamma0(t))*yp[1](t)*cos(alpha0(t))*sin(beta0(t))*cos(psi[1](t))*sin(theta[1](t))*l3[1]-2*sin(gamma0(t))*x0(t)*sin(alpha0(t))*sin(beta0(t))*sin(psi[1](t))*cos(theta[1](t))*l3[1]-2*sin(gamma0(t))*x0(t)*sin(alpha0(t))*sin(beta0(t))*cos(psi[1](t))*sin(theta[1](t))*l3[1]+2*sin(gamma0(t))*xp[1](t)*sin(alpha0(t))*sin(beta0(t))*sin(psi[1](t))*cos(theta[1](t))*l3[1]+2*sin(gamma0(t))*xp[1](t)*sin(alpha0(t))*sin(beta0(t))*cos(psi[1](t))*sin(theta[1](t))*l3[1]+2*cos(gamma0(t))*y0(t)*cos(alpha0(t))*sin(beta0(t))*sin(psi[1](t))*sin(theta[1](t))*l3[1]-2*cos(gamma0(t))*y0(t)*cos(alpha0(t))*sin(beta0(t))*cos(theta[1](t))*cos(psi[1](t))*l3[1]-2*cos(gamma0(t))*yp[1](t)*cos(alpha0(t))*sin(beta0(t))*sin(psi[1](t))*sin(theta[1](t))*l3[1]+2*cos(gamma0(t))*yp[1](t)*cos(alpha0(t))*sin(beta0(t))*cos(theta[1](t))*cos(psi[1](t))*l3[1]-2*cos(gamma0(t))*x0(t)*sin(alpha0(t))*sin(beta0(t))*sin(psi[1](t))*sin(theta[1](t))*l3[1]+2*cos(gamma0(t))*x0(t)*sin(alpha0(t))*sin(beta0(t))*cos(theta[1](t))*cos(psi[1](t))*l3[1]+2*cos(gamma0(t))*xp[1](t)*sin(alpha0(t))*sin(beta0(t))*sin(psi[1](t))*sin(theta[1](t))*l3[1]-2*cos(gamma0(t))*xp[1](t)*sin(alpha0(t))*sin(beta0(t))*cos(theta[1](t))*cos(psi[1](t))*l3[1]

Do you have some ideas so as to simplify this equation ?

N.B : Former posts on the topic of trigonometric simplification

http://www.mapleprimes.com/questions/209884-Simplification-Of-Trigonometric-Expression-II

http://www.mapleprimes.com/questions/209721-Simplification-Of-Trigonometric-Expressions

I put a worksheet attached in order to facilitate the troubleshooting.

Thanks a lot for your help

trigonometric_simplification.mw

 

Hello,

In the post :

http://www.mapleprimes.com/questions/209721-Simplification-Of-Trigonometric-Expressions

you have help me to build a procedure so as to simplify trigonometric expressions of the following form, that is to say where each trigonometric expression is in factor with a term :

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

From a mechanical point of view, this form of equations comes from the constraint equations obtained with a vectorial closure.

Now I would like to silmplify the constraint equations which come form angular closure.

The equations are in the form :

sin(gamma0(t))*cos(beta0(t)) = -(sin(psi[1](t))*cos(theta[1](t))*cos(gamma[1](t))+sin(psi[1](t))*sin(theta[1](t))*sin(gamma[1](t))-cos(theta[1](t))*cos(psi[1](t))*sin(gamma[1](t))+cos(psi[1](t))*sin(theta[1](t))*cos(gamma[1](t)))*cos(beta[1](t))

i try to treat the right side with the following code :

applyrule([
cos(u::anything)*cos(v::anything)-sin(u::anything)*sin(v::anything)=cos(u+v),
cos(u::anything)*sin (v::anything)+sin(u::anything)*cos(v::anything)=sin(u+v),
sin(u::anything)*sin(v::anything)-cos(u::anything)*cos(v::anything)=-cos(u+v),
-sin(v::anything)*cos(u::anything)-sin(u::anything)*cos(v::anything)=-sin(u+v)], simplify(-(sin(psi[1](t))*cos(theta[1](t))*cos(gamma[1](t))+sin(psi[1](t))*sin(theta[1](t))*sin(gamma[1](t))-cos(theta[1](t))*cos(psi[1](t))*sin(gamma[1](t))+cos(psi[1](t))*sin(theta[1](t))*cos(gamma[1](t)))*cos(beta[1](t)), size))

The result is :

(-sin(theta[1](t)+psi[1](t))*cos(gamma[1](t))+sin(gamma[1](t))*cos(theta[1](t)+psi[1](t)))*cos(beta[1](t))

It seems that the result is not simplified enough. I would like to obtain this expression :

cos(beta[1](t))*sin(gamma[1](t)-theta[1](t)-psi[1](t))

Have you a idea why the simplification is not conducted once more ? Do you have ideas so as to simplify the equation so as to obtain the result mentioned ?

Thanks a lot for your help

 

 

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