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Parametric motion
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Describe a path by x(t), y(t) and compute velocity by differentiation.
A path can be given by x(t), y(t). Velocity is (dx/dt, dy/dt) and acceleration the second derivatives. Eliminating t gives the shape of the path.
x = 2cos t, y = 2 sin t is a circle of radius 2; speed 2.
The same path can be travelled at different speeds.
In more detail
Parametric motion describes position as functions of a parameter, usually time, so each coordinate is given separately. It is a flexible way to describe curved paths.
Real-world uses
- Computer animation defines a character's path as parametric curves.
- Describing a cycloid, the path of a point on a rolling wheel.
- Computer animators describe a character's path with parametric equations, which gives position and velocity at every frame.
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Frequently asked questions
What is a parameter?
A variable, often time, that determines the position along the path.
How do I find the velocity?
Differentiate each coordinate with respect to the parameter.
What is a parametric equation?
An equation that gives x and y as functions of a third variable, usually time, so the path is traced as time passes.
Related topics in Kinematics
Rotational kinematics equations · Motion in polar coordinates · Motion in three dimensions · Galilean transformation · Frames: inertial vs non-inertial · Coriolis and fictitious motion