08-03-25.mw

>
 

Mostly we did math on the board today.  

 

> with(DEtools):
phug:= [ diff(theta(t),t) = ( v(t)^2 - cos(theta(t))) / v(t),
        diff(v(t),t)     = -sin(theta(t)) - R*v(t)^2 ];
 

>
 

[diff(theta(t), t) = `/`(`*`(`+`(`*`(`^`(v(t), 2)), `-`(cos(theta(t))))), `*`(v(t))), diff(v(t), t) = `+`(`-`(sin(theta(t))), `-`(`*`(R, `*`(`^`(v(t), 2)))))] (1)
 

> R:=1;
DEplot(phug, [ theta(t), v(t) ], t=0..40,
 

>        [[theta(0)=0, v(0)=2.5], [theta(0)=0, v(0)=.8]],
 

>        theta=-Pi/2..3*Pi, v=0..3,
 

>        linecolor=[blue,red], stepsize=0.1);
 

>
 

 

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