Cycloid - parametric equations and polar coordinates, Mathematics

Assignment Help:

Cycloid

The parametric curve that is without the limits is known as a cycloid.  In its general form the cycloid is,

X = r (θ - sin θ)

Y = r (1- cos θ)

 The cycloid presents the following situation. Refer a wheel of radius r.  Let the point in which the wheel touches the ground basically be called P.  Then start rolling the wheel to the right.  Like the wheel rolls to the right trace out the path of the point that is P.  The path which the point P traces out is called a cycloid and is specified by the equations above. In these equations we can think of θ as the angle by which the point P has rotated.

 Now here is a cycloid sketched out with the wheel shown at several places. The blue dot is the point P on the wheel that we were using to draw out the curve.

817_Cycloid - Parametric Equations and Polar Coordinates 1.png

From this diagram we can see that one arch of the cycloid is traced out in the range  0 < θ < 2π.   This makes sense while you consider that the point P will be back on the ground later it has rotated by an angle of 2π.


Related Discussions:- Cycloid - parametric equations and polar coordinates

Relationship between the graph and inverse function, Interesting relationsh...

Interesting relationship between the graph of a function and the graph of its inverse : There is one last topic that we have to address quickly before we leave this section.  Ther

Calculate probability, The following table contains some information about...

The following table contains some information about the model used. Assume the probabilities given by the model are those of being a good writer. Variable

Explain mixed numbers with examples, Explain Mixed Numbers with examples? ...

Explain Mixed Numbers with examples? Everybody loves a bargain, right? But sometimes these "special deals" aren't what they seem to be. For example, pretend you were at a

Find a maximum flow and a minimum cut, Use the maximum flow algorithm to fi...

Use the maximum flow algorithm to find a maximum flow and a minimum cut in the given network, where the capacities of arc CF, EC , DE and BD are w = 13, x = 7, y =1, a

Shares and dividend, how should i make my project on these topic?

how should i make my project on these topic?

Find the sum-of-products expression for the function, Find the sum-of-produ...

Find the sum-of-products expression for subsequent function,  F (x,y,z) = y + Z‾ Ans: The sum of the product expression for the following function f is DNF (disjunc

Homework, joey asked 30 randomly selected students if they drank milk, juic...

joey asked 30 randomly selected students if they drank milk, juice, or bottled water with their lunch. He found that 9 drank milk, 16 drank juice, and 5 drank bottled water. If the

Fractions, a boy is six months old his sister was given birth to three mont...

a boy is six months old his sister was given birth to three month after him. if their cousin is 0.33years old, arrange their ages in ascending order

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd