08-03-06.mw

> myeq:=y=3*x+7;
 

y = `+`(`*`(3, `*`(x)), 7) (1)
 

> solve(myeq,{x});
 

{x = `+`(`*`(`/`(1, 3), `*`(y)), `-`(`/`(7, 3)))} (2)
 

> solve(y=3*x+7,{x});
 

{x = `+`(`*`(`/`(1, 3), `*`(y)), `-`(`/`(7, 3)))} (3)
 

>
 

>
 

> with(DEtools):
 

> R:='R';
phug:= [ diff(theta(t),t) = ( v(t)^2 - cos(theta(t))) / v(t),
        diff(v(t),t)     = -sin(theta(t)) - R*v(t)^2 ];
 

 

R
[diff(theta(t), t) = `/`(`*`(`+`(`*`(`^`(v(t), 2)), `-`(cos(theta(t))))), `*`(v(t))), diff(v(t), t) = `+`(`-`(sin(theta(t))), `-`(`*`(R, `*`(`^`(v(t), 2)))))] (4)
 

> R:=0;DEplot( phug, [ theta(t), v(t) ], t=0..6,
 

>        [seq([theta(0)=0, v(0)=0.5+2*i/10], i=0..10)],
 

>        theta=-Pi/2..2*Pi, v=0..3,
 

>        linecolor=[seq(COLOR(HUE, i/10), i=0..10)]);
 

>
 

>
 

 

0
Plot_2d
 

> R:=0;DEplot( phug, [ theta(t), v(t) ], t=0..6,
 

>        [seq([theta(0)=0, v(0)=0.5+2*i/10], i=0..10)],
 

>        theta=-Pi/2..2*Pi, v=0..3,
 

>        linecolor=[seq(COLOR(HUE, i/10), i=0..10)], method=classical[foreuler],
     stepsize=1);
 

>
 

>
 

 

0
Plot_2d
 

> DEplot( phug, [ theta(t), v(t) ], t=0..6,
 

>        [seq([theta(0)=0, v(0)=0.5+2*i/10], i=0..10)],
 

>        theta=-Pi/2..2*Pi, v=0..3,
 

>        linecolor=[seq(COLOR(HUE, i/10), i=0..10)], method=classical[foreuler],
       stepsize=.1);
 

>
 

Plot_2d
 

> DEplot( phug, [ theta(t), v(t) ], t=0..6,
 

>        [seq([theta(0)=0, v(0)=0.5+2*i/10], i=0..10)],
 

>        theta=-Pi/2..2*Pi, v=0..3,
 

>        linecolor=[seq(COLOR(HUE, i/10), i=0..10)], method=classical[rk4],
       stepsize=.1);
 

>
 

Plot_2d
 

> R:=0.1;
 

> DEplot( phug, [ theta(t), v(t) ], t=0..6,
 

>        [seq([theta(0)=0, v(0)=0.5+2*i/10], i=0..10)],
 

>        theta=-Pi/2..4*Pi, v=0..3,
 

>        linecolor=[seq(COLOR(HUE, i/10), i=0..10)], method=classical[rk4],
       stepsize=.1);
 

>
 

 

.1
Plot_2d
 

> DEplot( phug, [ theta(t), v(t) ], t=0..20,
 

>        [[theta(0)=0,v(0)=2]],
 

>        theta=-Pi/2..8, v=0..3,
 

>        linecolor=[seq(COLOR(HUE, i/10), i=0..10)], method=classical[rk4],
       stepsize=.01);
 

>
 

Plot_2d
 

>
 

>