Items tagged with parametric

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I have a parametric equation which want to solve it , but maple does not .

problem.mw

 best regards

Dear MaplePrimes team,

 

For display a beautiful parametric surface with hole (or pierced surface), unfortunately unlike CAD (computer-aided design) tool, Maple requires a large grid number. Therefore the computing is too long and requires huge RAM only with grid of [500,500] on a modern computer.

      

Fig. 1: For a complex surface such an aircraft fuselage here, Needs high grid, therefore, the compilation is too long with modern computer (Intel Core i7, 2.4 GHz CPU, 16 GB RAM). If displays supplementary windows holes on fuselage, the software may bug when the RAM is full.

 

Question 1:

In matter of low cost computation, do you have better solution to create a fast surface with smooth hole from given a parametric surface equation S(x,y) and given any convex/concave-closed parametric curve C(t) that is projected on surface S(x,y)?

Fig. 2: These surfaces are been created in Maple 2016 from given initial parametric surface equation and curve projected on the surface. But requires huge grid, huge RAM, and long time to get smooth hole when free CAD tools are fast and low RAM.

 

Question 2:

Because I noted that the Maple’s view option renderers smooth edges of any surface. My question is: Is it possible to use the internal structure of display/view used by Maple to apply at free boundaries? I think it will be possible to create many class of view, for examples: cylindrical sector, spherical sector views or more rather to be limited with conventional cubic view. And thus, I think it will be possible to create own smooth hole or multiple-hole on surface and get smooth pierced surface.

 

I know that almost of technicians/engineers will recommend me to use a CAD tool to create surface with hole. But the objective here is to keep purely a mathematical mind and work with exact equations (analytic equations).

On a free CAD tool, even the complex holes are created very fast only with low RAM. Why not on Maple?

 

Best.

 

Guy.

Parametric equation of a circle in 3d by three points. Draghilev method.

CIRCLE_3_POINTS_geom3d_2.mw

In manual solution is no problem, but i am interest to compute it with any software such maple since i am not familiar, How to find solution in term of parametric equation a(r), b(r), c(r) for r=-5..5 and also visualize this three derivative condition? d(a)=a+b+c, d(b)=a-b+c, d(c)=a-b-c

 

i want parametrix answer for z in terms of w, what should i do ? please help

 

 

``

restart:

P:=w-10*z-1/5*z^2-1/200*z^3-1/500*z^4-z^5-1/1000*z^6

w-10*z-(1/5)*z^2-(1/200)*z^3-(1/500)*z^4-z^5-(1/1000)*z^6

(1)

solve(P,z)

RootOf(_Z^6+1000*_Z^5+2*_Z^4+5*_Z^3+200*_Z^2+10000*_Z-1000*w)

(2)

 

 

 

``

 

Download solve.mw

Hi!!

 

I am trying to plot the above curve:

 

restart; with(plots)

> f0 := proc (t) options operator, arrow; t, (-1)*3.9*t*(t-1) end proc; 

> IFS := proc (i, x, y) if i = 1 then return (1/2)*y, (1/2)*x end if; if i = 2 then return (1/2)*x, (1/2)*y+1/2 end if; if i = 3 then return (1/2)*x+1/2, (1/2)*y+1/2 end if; if i = 4 then return -(1/2)*y+1, -(1/2)*x+1/2 end if end proc; 

> g := proc (t) local j; for j to 4 do if evalf((1/4)*j-1/4) <= evalf(t) and evalf(t) <= evalf((1/4)*j) then return IFS(j, f0(4*t-j+1)); break end if end do end proc; 

 

Thus, the instruction  parametricplot(['g'(t),t=0..1]) return the message  

Error, (in plot) incorrect first argument [g(t), t = 0 .. 1]

Some idea or hit to plot this?

 

Thank you for your time

 

hi.how i can determind  eignvalue of matrix in the form parametric?

thanks1.mw

T := Matrix(5, 5, {(1, 1) = -b*beta*k/(c*u)-d, (1, 2) = 0, (1, 3) = -beta*lambda*c*u/(b*beta*k+c*d*u), (1, 4) = 0, (1, 5) = 0, (2, 1) = b*beta*k/(c*u), (2, 2) = -s*(lambda*c*k*beta/(b*beta*k+c*d*u)-a)/P-a, (2, 3) = beta*lambda*c*u/(b*beta*k+c*d*u), (2, 4) = -s*b/c, (2, 5) = r*(s-p)/s, (3, 1) = 0, (3, 2) = k, (3, 3) = -u, (3, 4) = 0, (3, 5) = 0, (4, 1) = 0, (4, 2) = -s*(lambda*c*k*beta/(b*beta*k+c*d*u)-a)/P, (4, 3) = 0, (4, 4) = -s*b/c-b, (4, 5) = r*(s+c)/s, (5, 1) = 0, (5, 2) = s*(lambda*c*k*beta/(b*beta*k+c*d*u)-a)/P, (5, 3) = 0, (5, 4) = s*b/c, (5, 5) = -r})

Matrix(5, 5, {(1, 1) = -b*beta*k/(c*u)-d, (1, 2) = 0, (1, 3) = -beta*lambda*c*u/(b*beta*k+c*d*u), (1, 4) = 0, (1, 5) = 0, (2, 1) = b*beta*k/(c*u), (2, 2) = -s*(lambda*c*k*beta/(b*beta*k+c*d*u)-a)/P-a, (2, 3) = beta*lambda*c*u/(b*beta*k+c*d*u), (2, 4) = -s*b/c, (2, 5) = r*(s-p)/s, (3, 1) = 0, (3, 2) = k, (3, 3) = -u, (3, 4) = 0, (3, 5) = 0, (4, 1) = 0, (4, 2) = -s*(lambda*c*k*beta/(b*beta*k+c*d*u)-a)/P, (4, 3) = 0, (4, 4) = -s*b/c-b, (4, 5) = r*(s+c)/s, (5, 1) = 0, (5, 2) = s*(lambda*c*k*beta/(b*beta*k+c*d*u)-a)/P, (5, 3) = 0, (5, 4) = s*b/c, (5, 5) = -r})

(1)

``

 

Download 1.mw

 

How I can solve it ? If I want a solution dependent of a. With fsolve? But how?

-x3+ax2-lnx=0
 

Suppose I have a function like this: f=cos(2t/m)+cos(2(t+5)/m).

 

Now for each fixed m, we get the maximum value of f. Then I want to build a plot where x-axis is m and y-axis is f, how could I do that? Please help!

 

Hello,

I would like to build a periodic curve but starting from a parametric curve and not with a function.

Thanks to you tips, I could obtain a periodic function with a piecewise function starting from a function (http://www.mapleprimes.com/questions/208795-Periodic-Piecewise-Function)

I would like to do the same approach but starting from this parametric curve f :

V:=Vector([cos(t),sin(t)]);
f:=unapply(V, t);
plot( [f(t)[1],f(t)[2], t = 0..evalf(Pi)],color=red, scaling=constrained);

And I would like to build a periodic curve (the period is defined on the x axis) g such as :

 

Unfortunately, the approach presented in the post http://www.mapleprimes.com/questions/208795-Periodic-Piecewise-Function does'nt work anymore.

Do you have ideas to build this periodic curve starting from the parametric curve defined above ?

The aim of my question is more linked to the methodolody than the result.

Thank you for your help.

How I can sketch the helix with parametric equations x=2cost  y=sint  z=t  and the line with parameric equation x=-2t  y=1  z=(pi/2)+t   on a three-dimensional coordinate system?

Suppose I have the parametric equations of a circle

x=cost

y=sint

where t runs from 0 to 2*pi. How can I show the orientation of this parametric curve on a plot?

we have a curve (x^2+y^2)^2=x^2-y^2

parametric representation of the curve is given by

x(t)=cos(t)/1+sin^2(t)

y(t)=sin(t)cos(t)/1+sin^2(t)

 

and we are asked to plot the curve using a parametric plot for -Pi<t<Pi

Hi!

For my lecture advanced dynamics, I got the question to make a sketch of the coordinate system and the particle’s motion, with the following position vector:

r(t) = (a cos(ωt))i + (b sin(ωt))j + (ct)k

In this function, ω is in [rad/s], a and b are in [m], t in [s] and c is [m/s].

I have no idea what this should look like, and I was thinking about plotting this with Maple, but thus far I'm not succeeding in plotting it. Which function or method can I use to visualize this in Maple?

Thanks a lot!

 

Hello everybody

In the attached file, I tried to solve the system of equations and obtain the parametric solution for my unknowns that are A1, A2, A3, A4, A5, A6, A7 and A8. I have 8 equations and 8 unknowns. The other variables are all known and parametric. I thought Maple could solve these system of equations easily but when I ran the program and waited for about 2 hours, unfortunately it returned no answer and it was in evaluating mode and I closed the program forcely. Does my file have any problem or Maple cannot solve these system of equations.

Thanks in advance

SOE.mw

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