rlewis

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These are questions asked by rlewis

Based on information I learned here last week, I tried the following.  Summary: I enter three functions f,g,h. f Is a function of x and t, g is a function of y and t, h of z and t.  I want to plot a 3D curve. I know an intial value.  The curve looks good but quite very early saying "cannot evaluate the solution further right of 3.4774922, probably a singularity."  HELP!

f := 4.61376*x+1.320192000*cos(t)^2*x-.320192000*sin(t)*cos(t)^2*x+4.304656800*cos(t)^2*x^2+17.21862720*cos(t)*x^2+12.9477168*sin(t)^2*x^2-25.8954336*sin(t)*x^2+7.147008*sin(t)^3*x-21.441024*sin(t)^2*x+9.68025600*sin(t)*x+3.181248*sin(t)*x^3-1.3251456*sin(t)*cos(t)^2+2.6502912*sin(t)^2*cos(t)+0.6625728*sin(t)^2*cos(t)^2+5.2807680*cos(t)*x-5.3005824*sin(t)*cos(t)+0.9443529*x^4-3.181248*x^3+147.0230064*cos(t)^2+67.10736960*sin(t)^2+23.693094*x^2+6.8757264*cos(t)^4-61.58338560*sin(t)^3-11.047968*sin(t)+15.3958464*sin(t)^4+148.045536*cos(t)+55.0058112*cos(t)^3-5.2807680*sin(t)*cos(t)*x+38.16801;


g := 0.9443529*y^4-42.29607960*y^2-3.437942400*y^3-1.3314096*sin(t)^2*y^2+2.662819200*sin(t)*y^2-17.5101696*sin(t)^3*y+52.530508800*sin(t)^2*y+25.45344*cos(t)^2*y+3.437942400*sin(t)*y^3-11.85948*cos(t)^2*y^2-47.43792*cos(t)*y^2-138.4682688*sin(t)*y+101.81376*cos(t)*y-101.81376*sin(t)*cos(t)*y-25.45344*sin(t)*cos(t)^2*y+632.4697764-91.635840*sin(t)*cos(t)^2+183.27168*sin(t)^2*cos(t)+45.8179200*sin(t)^2*cos(t)^2-366.5433600*sin(t)*cos(t)+942.16392*cos(t)^2+247.7287584*sin(t)^2+39.20400*cos(t)^4-61.5833856*sin(t)^3-372.2907456*sin(t)+15.3958464*sin(t)^4+1259.59968*cos(t)+313.63200*cos(t)^3+103.4479296*y; 
h := z-2*sin(t)+2;
eqs := {f, g, h};
eqs2 := subs(x = x(t), y = y(t), z = z(t), eqs);
x0 := -0.896661124832438;
y0 := -1.7877356703982348;
z0 := -2;
ics := {x(Pi) = x0, y(Pi) = y0, z(Pi) = z0};
odes := diff~(eqs2, t);
res := dsolve(odes union ics), numeric);
plots:-odeplot(res, [x(t), y(t), z(t)], Pi .. 2*Pi); p1 := %;

A good graph is produced of maybe 10% of the answer.  Then:

Warning, cannot evaluate the solution further right of 3.4774922, probably a singularity

 

 

For example, 

f(x,t) = t^2 x^2 + t x + 2x - 1g(y,t) = t^2 y^3 + t y^2 + 2y - 1h(z,t) = 2t^2 z^3 + t z + 3z - t^2, 0 < t < 4.

I have an initial point on the curve corresponding to t=0.  The answer is a curve in space, or maybe several curves.  The real example that I care about is much more complex than this and has trig functions of t.

I am modeling a molecule.  I have six line segments.  I know the coordinates of their ends as functions of time.  Naively, I would think it would go like this:

define some functions (composites of trig functions, rational functions, etc)

define points 1,2, ..., 6.   (in terms of the functions)

define line1, line2, ...., line6

define structure = union of 6 lines

animate(structure) as t goes from t_0, ..., t_1

How exactly do i do this?

I have two parametric equations, one for x(t), one for y(t).  Both are ODEs of order 1.  Both are implicit.  There is no way to solve explicitly for dx/dt or dy/dt.  How can I get Maple to do a plot of the solution?  I tried DEplot but apparently it demands an explicit presentation of dx/dt and dy/dt.   I have Maple12 on a Mac, but could use Maple15 on a server.

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