ZhuWeihong

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10 years, 62 days

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These are questions asked by ZhuWeihong

this error message hapened,but  i try process agin ,this erro disappeared, the proce is perfect, but  then it appear agin. is this a bug?  i use maple 16.

> restart;
> with(plots);
> with(DEtools);
> pendulums := proc (L, angle, velocity, a, b, n) local i, deq, X, Y, inits, slnnf, ACF1, ACF2, ACF3, ACF4; deq := L*(diff(theta(t), `$`(t, 2)))+(diff(X(t), `$`(t, 2)))*cos(theta(t))+(diff(Y(t), `$`(t, 2))+9.81)*sin(theta(t)) = 0; inits := {theta(0...

i creat an animation in maple , and want to export it then use it in other presentation, such as word or powerpoint.

i try to save the animation, but fail, it is only one static picture, so how can i export it dymaticlally.

today, i stuty a differential equation,  firsy, i conver the equation from cartesian to polar as  follow:

restart: 

sys := diff(x(t), t) = -y(t)+x(t)*(1-2*x(t)^2-3*y(t)^2), diff(y(t), t) = x(t)+y(t)*(1-2*x(t)^2-3*y(t)^2):

then  using transformation x=r*cos(theta),y=r*sin(theta) convert it to polar coordinate,and get:

sys1:=diff(r(t), t) = r(t)*(1-2*r(t)^2-r(t)^2*sin(theta(t))^2), diff(theta(t), t) = 1

then  plot the phase portrait, i use to method ,but all of them failed:

first ,use DEplot

  with(DEtools): 

 DEplot(sys1, [theta(t), r(t)], t = 0 .. 10, [[theta(0) = 2, r(0) = 2]], coords = polar);

and get error:
Error, (in DEtools/DEplot) can only plot in cartesian co-ordinates, got invalid option coords = polar

second,use odeplot

   with(plots):

> q1 := dsolve([diff(r(t), t) = r(t)*(1-2*r(t)^2-r(t)^2*sin(theta(t))^2), diff(theta(t), t) = 1, theta(0) = Pi, r(0) = 2], numeric, [theta(t), r(t)]);

> with(plots);

> odeplot(q1, [r(t), theta(t)], t = 0 .. 1, numpoints = 500, axiscoordinates = polar, coords = polar);

and also get a wrong result, so how to plot the phase portrait in polar coordinate using DEplot or odeplot

 

i study a simple differential equations as follow and get the solution,but i faced two warning which puzzle me:

> restart;
> eq2 := diff(x(t), t) = x(t), diff(y(t), t) = x(t)^2+y(t)^2-1;
   ans1 := dsolve({eq2, x(0) = 1, y(0) = -1}, numeric, [x(t), y(t)], range = -10 .. 10)       ;

Warning, cannot evaluate the solution further left of -1.1646698, probably a singularity

there are four points :

O = (0, 0), P = (0, b/d), Q = (beta/delta, 0), R = ((-d*beta+b*gamma)/(-delta*d+gamma*c), (beta*c-delta*b)/(delta*d-gamma*c))

and then  define the jocbian maxtrix as

J=Matrix(2, 2, {(1, 1) = beta-2*delta*x-gamma*y, (1, 2) = -x*gamma, (2, 1) = -y*c, (2, 2) = b-2*d*y-c*x})

at last , i want to get the jocbian matrix at the four points,  so  must substitute the coordinate of the four point into the...

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