Parameterization of the Circle

  • Thread starter vanitymdl
  • Start date
  • Tags
    Circle
In summary, the conversation discusses the parameterization of a circle using three different equations and the task of finding the time it takes for a particle to travel from point (1,0) to (0,1) for each parametrization. The proposed solution involves finding a value of t for which x(t) equals (1,0) and then finding the next greater value of t for which x(t) equals (0,1).
  • #1
vanitymdl
64
0

Homework Statement



Consider the following parameterization of the circle:
a) x1 (t) = (cost, sint)

b) x2 (t) = (cos3t, sin3t)

c) x3 (t) = (sint, cost)

How long does it take point a particle to go from (1,0) to (0,1) for each parameterization.

Homework Equations





The Attempt at a Solution


(cos,sin) of (1,0) is 2pi then (cos, sin) of (0,1) is pi/2

how would I figure out the time it takes?
 
Physics news on Phys.org
  • #2
vanitymdl said:

Homework Statement



Consider the following parametrization of the circle:
a) x1 (t) = (cost, sint)

b) x2 (t) = (cos3t, sin3t)

c) x3 (t) = (sint, cost)

How long does it take point a particle to go from (1,0) to (0,1) for each parametrization.

Homework Equations



The Attempt at a Solution


(cos,sin) of (1,0) is 2pi then (cos, sin) of (0,1) is pi/2

how would I figure out the time it takes?
For each parametrization find a value of t for which x(t) = (1, 0), then find the next greater value of t for which x(t) = (0, 1) .
 
  • #3
Tricky wording. :smile:
 

FAQ: Parameterization of the Circle

1. What is the purpose of parameterization of the circle?

The purpose of parameterization of the circle is to represent points on a circle using parameters or variables. This allows for easier calculations and analysis of the circle's properties.

2. How is the circle parameterized?

The circle can be parameterized using either Cartesian coordinates or polar coordinates. In Cartesian coordinates, the circle can be represented as (x,y) where x = r cos θ and y = r sin θ. In polar coordinates, the circle can be represented as (r,θ) where r is the radius and θ is the angle measured from the positive x-axis.

3. What is the equation for parameterization of the circle?

The equation for parameterization of the circle is x = r cos θ and y = r sin θ, where r is the radius and θ is the angle measured from the positive x-axis.

4. What are the advantages of parameterization of the circle?

Parameterization of the circle allows for easier calculations and graphing of the circle's properties. It also allows for the representation of a point on the circle using only two variables, making it more efficient.

5. How is parameterization of the circle used in real-world applications?

Parameterization of the circle is used in various fields such as physics, engineering, and computer graphics. It is used to model circular motion, calculate forces acting on a circular object, and create 3D circular shapes in computer graphics.

Back
Top