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

Simulation and Modeling, I have some sample simulation and modeling practic...

I have some sample simulation and modeling practice questions using isee Stella software.

Free - undamped vibrations, It is the simplest case which we can consider. ...

It is the simplest case which we can consider. Unforced or free vibrations sense that F(t) = 0 and undamped vibrations implies that g = 0. Under this case the differential equation

Transportation problem, matlab code for transportation problem solved by vo...

matlab code for transportation problem solved by vogel''s approximation method

Application of probability in business, Application of Probability in Busin...

Application of Probability in Business 1. Business games of chance for illustration, Raffles Lotteries. 2. Insurance firms: this is generally done when a new client or prop

Operation research, Advantages and disadvantages of operation researchs

Advantages and disadvantages of operation researchs

Differential equation, Question: In the interest of saving up enough mo...

Question: In the interest of saving up enough money for retirement, you have created a bank account to store a  sum of money. Compound interest on  this account is accumulated

Factorization of expressions, Above we have seen that (2x 2 - x + 3)...

Above we have seen that (2x 2 - x + 3) and (3x 3 + x 2 - 2x - 5) are the factors of 6x 5 - x 4 + 4x 3 - 5x 2 - x - 15. In this case we are able to find one facto

What is monomials and polynomials in maths, What is Monomials and Polynomia...

What is Monomials and Polynomials in maths? An expression like 7x is called a monomial. A monomial is an integer, a variable, or a product of integers and variables. Other e

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