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

Hi. I'm hacing trouble writing a maple procedure for the question below, can anyone help?

Write a maple procedure which takes as its input the vectoeat u1 and u2 and the eigenvectors lambda1 and lambda2 where u1,u2 are element of R^2 and the lambdas are real numbers.

If u1,U2 is linearly independent then the output is the matrix A an element of R^2x2 with the property that Au1= lambda1u1 and AU2=lambda2u2;

if u1,u2 is linearly dependent then the output is the statement "not an eigenbasis".

I I then have two inputs which I have to do but I'm not sure on how to write the procedure. Any help will be much appreciated.  

Thanks :)

Dear all,

I developed a program to solve f(x, y) = 0 and g(x, y) = 0, I obtained as results (x=2.726, y=2.126) . running the same program another time it gives (x=2.762, y=1.992). how to explain this?

> fsolve({f(x, y) = 0, g(x, y) = 0}, {x = 0 .. infinity, y= 0 .. infinity});

Thanks in advance.

after solved, 

diff(a(t), t) = diff(a(t), t)

diff(b(t), t) = 0

diff(c(t), t) = -b(t)/c(t)

there is a diff(a(t), t) term 

how to plot this kind of system?

can diff(a(t), t) be ignore so that only consider two equations, diff(b(t),t) and diff(c(t),t) ?

if so, i use below to plot, it can not show the arrow clearing , i can only see arrow near origin, but not far point

with(plots):
fieldplot([0, y/x], x = -2 .. 2, y = -2 .. 2);
fieldplot([0, y/x], x = -2 .. 2, y = -2 .. 2, arrows = SLIM,grid = [1, 1]);
fieldplot([0, y/x], x = -10 .. 10, y = -10 .. 10);

 about how to calculate vector field of system of 3 differential equations which in terms of a(t), b(t), c(t) , diff(a(t),t), diff(b(t),t), diff(c(t),t)?

is the only method is the express diff(a(t),t), diff(b(t),t), diff(c(t),t) in terms of a(t), b(t), c(t) ?

for example 

<diff(a(t),t), diff(b(t),t), diff(c(t),t)>

if result is

diff(a(t),t) = a(t)*b(t)

diff(b(t),t) =b(t)*c(t)

diff(c(t),t) =c(t)*a(t)

<a(t)*b(t), b(t)*c(t), c(t)*a(t)>

then

is it the vector field <a*b, b*c, c*a> ?

When I put maximize(cos(t)), everything is fine.

When I put maximize(cos(Pi)), everything is fine.

When I put maximize(cos(t*Pi)), it says invalid limiting point??? What went wrong?

Hello,

I want to solve a optimization problem with maple/maplesim.

A car has to move a defined distance on a plane, straight road in a defined time. Given is the mass of the car, the maximum force to accelerate the car, the distance and the time. The rolling resistance and the drag force should be considered. At start-point speed v = 0m/s and also at the end-point speed should be v= 0m/s.

So there are the following model parameters:

mass                            m = 2000kg
distance                        d  = 1000m
time                              t_max = 120s
                                    v_0 = 0m/s
                                    v_d = 0m/s
accelerating force           -1m/s² <= F_acc/m <= 1m/s²
resistance to rolling        F_rol = C + A*v²                      C and A are later defined
resulting force at mass   F_res = F_acc - F_rol

The energy consumption  integral F_acc(s) ds (from 0 to d) should be minimized and I want to print the graph of F_acc(s) 

How can or can Maple help me solving this optimization problem?

I'm looking for the 3-D integral formulae for Convolution, and Cross Correlation, between pairs of functions, which are each in spherical polar coordinates, for implementation in a MAPLE worksheet. Each function is normalized and symmetric around the origin.

Thank you for your consideration.

sys := {diff(b(t),t) = 0,diff(c(t),t) = -b(t)/a(t)};
DEplot(sys, [b(t),c(t)], t=0..5, x=-5..5, y=-5..5);
Error, (in DEtools/DEplot) Option keyword (x) was not in the allowed set of options, consisting of: iterations, arrows, dirgrid, obsrange, scene, colour, linecolour, stepsize, a dependent variable range, a list of initial conditions or one of the allowed plot options: {animate, axes, color, colour, coords, font, scaling, style, symbol, title, view, animatecurves, animatefield, axesfont, dirfield, labelfont, linestyle, numframes, resolution, thickness, tickmarks, titlefont, xtickmarks, ytickmarks}, or one of the allowed dsolve/numeric options: {abserr, control, ctrl, initial, itask, maxder, maxfun, maxkop, maxord, maxpts, maxstep, method, mi..

diff(a(t), t) = diff(a(t), t);
diff(b(t),t) = 0;
diff(c(t),t) = -b(t)/a(t);

[diff(rhs(sol[1][2]), a(t)),diff(rhs(sol[1][2]), b(t)),diff(rhs(sol[1][2]), c(t))];
Error, (in VectorCalculus:-diff) invalid input: diff received a(t), which is not valid for its 2nd argument

hey guys Im new client in maple and today I was about check out the resualt of my mathematic quastion with maple.

I need a step by step solution and exact command to give me true resualts 

for example 

how can I expand a factorization like (x^2-y^2) to (x-y)(x+y)

in a little more  complicated form (cd-1)^2-(c-d)^2/(d^2)(c-1)=5 the value of c=?

for solve this problem I need to expand (cd-1)^2-(c-d)^2 than other expands & in the end value of c

I dont have anymore time for my mathemathic exam so know that how maple works in basic and intermadiate mathematic level is important to me

thank you guys

eq2 := b(t)*(diff(c(t), t))*(diff(a(t), t))+b(t)*(diff(a(t), t))+a(t)*(diff(c(t), t));
eq3 := a(t)*(diff(b(t), t))(diff(a(t), t))+b(t)*(diff(b(t), t))*(diff(c(t), t));
eq4 := b(t)*(diff(c(t), t))(diff(b(t), t))+a(t)*(diff(b(t), t))+b(t)*(diff(c(t), t));
dfieldplot([eq2,eq3,eq4],[t,x],t=0..5,a=-5..5,b=-5..5,c=-5..5);
dfieldplot([eq2,eq3],[t,x],t=0..5,a=-5..5,b=-5..5);
eq2a := eval(subs(c(t)=exp(t), eq2));
eq3a := eval(subs(c(t)=exp(t), eq3));
eq4a := eval(subs(c(t)=exp(t), eq4));
dfieldplot([eq2a,eq3a], [a(t), b(t)], t = -5 .. 5, a = -5 .. 5, b = -5 .. 5, arrows = SLIM, color = black, dirfield = [10, 10]);

Hey,

I think I found a bug concerning the useage of assume and alias:

Commenting out the alias command produces correct results. I am on linux with build 922027.

alias_bug.mw

I want to solve a system of equations using f-solve (two unknowns) and exporting the solutions to a matrix where the solutions are in seperate columns. How do I do this?

I have tried:

for i from 1 to 937 do

AP[i,1]:=fsolve(x=KL[i,1].y=KL[i,2],x=..8,y=0..15))

end if

end do

But this returns the solutions for X and Y in the same column. Also, for the values that are not possible to solve, it returns the entire expression instead of e.g. 0 or "undefined".

Thank you.

 from determinant's polynomial?