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

Write down the first few terms of the sequences, Write down the first few t...

Write down the first few terms of each of the subsequent sequences. 1. {n+1 / n 2 } ∞ n=1 2. {(-1)n+1 / 2n} ∞ n=0 3. {bn} ∞ n=1, where bn = nth digit of ? So

Algebra, solutions for the equation a-b=5

solutions for the equation a-b=5

Linear programming problem, I have a linear programming problem that we are...

I have a linear programming problem that we are to work out in QM for Windows and I can''t figure out how to lay it out. Are you able to help me if I send you the problem?

Probability, An unbiased die is tossed twice .Find the probability of getti...

An unbiased die is tossed twice .Find the probability of getting a 4,5,6 on the first toss and a 1,2,3,4 on the second toss

Explain that odd positive integer to be a perfect square, Show that for odd...

Show that for odd positive integer to be a perfect square, it should be of the form 8k +1. Let a=2m+1 Ans: Squaring both sides we get a2 = 4m (m +1) + 1 ∴ product of two

Exponents., the (cube square root of 2)^1/2)^3

the (cube square root of 2)^1/2)^3

The value of m+n, Every point (x,y) on the curve y=log2 3x is transferred t...

Every point (x,y) on the curve y=log2 3x is transferred to a new point by the following translation (x',y')=(x+m,y+n), where m and n are integers. The set of (x',y') form the curve

Estimate the temperature, The temperature at midnight was 4°F. Through 2 A....

The temperature at midnight was 4°F. Through 2 A.M. it had dropped 9°F. What was the temperature at 2 A.M.? If the temperature is only 4° and drops 9°, it goes below zero. It d

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