Samples of parametric equations

In summary, there are many useful and famous parametric equations in math, physics, and engineering. Some examples include the cycloid, epicycloid, hypocycloid, and hypotrochoid. These equations can be used to describe shapes such as ellipses and can also be used in applications such as spirographs. Other interesting loci that can be described by parametric equations include the cardioid and the spiral of Archimedes. These equations provide a powerful tool for describing curves and shapes in various fields of study.
  • #1
xyz3003
5
0
I need samples of parametric equations:
x=Fx(t);
y=Fy(t);

the samples must be useful or famous in math, physics or engineer, not be created randomly meaningless.

one that I know is to describle ellipse:
x=A*cos(t);
y=B*sin(t);

I need 2 or more good samples for my report.

thanks.

found so far:

Cycloid
Epicycloid
Hypocycloid
Hypotrochoid
Spirograph
 
Last edited:
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  • #2
A cycloid is a good example. Look it up.
 
  • #3
nicktacik,
thanks.
by your clue, i found a set of them:

Cycloid
Epicycloid
Hypocycloid
Hypotrochoid

I add them in my post and will use them soon.

Any other interesting locus?
 

1. What are parametric equations?

Parametric equations are a set of equations that describe the relationship between two or more variables in terms of one or more parameters. They are commonly used in mathematics and physics to describe complex curves and surfaces.

2. How are parametric equations different from standard equations?

Parametric equations use parameters to define the relationship between variables, whereas standard equations directly relate variables to each other. This allows for more flexibility and complexity in describing curves and surfaces.

3. What are some applications of parametric equations?

Parametric equations are used in various fields, such as physics, engineering, and computer graphics. They are commonly used to describe the motion of objects, the shape of curves and surfaces, and the behavior of complex systems.

4. How do you graph parametric equations?

To graph parametric equations, you can plot points by substituting different values for the parameters and then connecting them to form a curve or surface. Alternatively, you can use a graphing calculator or computer program to plot the equations directly.

5. What are some common examples of parametric equations?

Some common examples of parametric equations include the equations for a circle, a parabola, and a helix. They are also used to describe conic sections, such as ellipses and hyperbolas, and other complex curves and surfaces.

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