Solving the cycloid equation

Question

The equations are:

$x=r(t-\sin{t})$

$y=r(1-\cos{t})$

Lets say that $(x,y)=(1,2)$ for a point. How can I find the radius of the cycloid? I can't solve the mathematics equation: $$\frac{1}{t-\sin{t}}=\frac{2}{1-\cos{t}}$$

It's complicate for me to solve it. If I'll find it I would find $r$.

thanks

score 1 · Answer 1 · answered Jul 17 '17 at 16:28

1

HINT: you have the equation $$1-\cos(t)=2t-2\sin(t)$$ then $t=0$ is one solution the other solution can be obtained by a numerical method, $$t\approx 1.401379455902473454923964650592$$

answered Jul 17 '17 at 16:28

Dr. Sonnhard Graubner

95,283

That's exactly what i wanted to know. How you solved it? I'll be glad if you have an explanation for the full solution – Electrician Jul 17 '17 at 16:30
there is the Newton-Raphson method Google for it – Dr. Sonnhard Graubner Jul 17 '17 at 16:31
OK, but what will be my start number (t0) in this case? – Electrician Jul 17 '17 at 17:42
take your calculator plot the equation and you will get a startnumber – Dr. Sonnhard Graubner Jul 17 '17 at 17:47
And for a more global case, if want the shortest trajectory from a to b according to the cycloid solution, the radios will be figure from (x,y) of a or b? – Electrician Jul 17 '17 at 18:00

Solving the cycloid equation

1 Answers1