Planar Motion
by Mitch Shindelbower
Title
Planar Motion
Artist
Mitch Shindelbower
Medium
Photograph
Description
Planar motion
While all motion in a mechanical system occurs in three dimensional space, planar motion can be analyzed using plane geometry, if all point trajectories are parallel to a plane. In this case the system is called a planar mechanism (or robot). The kinematic analysis of planar mechanisms uses the subset of SE(3) consisting of planar rotations and translations, denoted SE(2).
The group SE(2) is three dimensional, which means that every position of a body in the plane is defined by three parameters. The parameters are often the x and y coordinates of the origin of a coordinate frame in M measured from the origin of a coordinate frame in F, and the angle measured from the x-axis in F to the x-axis in M. This is described saying a body in the plane has three degrees-of-freedom. SE(2) is the configuration space for a planar body, and a planar motion is a curve in this space. In physics, motion is a change in position of an object with respect to time and its reference point. Motion is typically described in terms of displacement, direction, velocity, acceleration, and time.[1] Motion is observed by attaching a frame of reference to a body and measuring its change in position relative to that frame.
A body which does not move is said to be at rest, motionless, immobile, stationary, or to have constant (time-invariant) position. An object's motion cannot change unless it is acted upon by a force, as described by Newton's first law. An object's momentum is directly related to the object's mass and velocity, and the total momentum of all objects in a closed system (one not affected by external forces) does not change with time, as described by the law of conservation of momentum.
As there is no absolute frame of reference, absolute motion cannot be determined.[2] Thus, everything in the universe can be considered to be moving.[3]
More generally, the term motion signifies a continuous change in the configuration of a physical system. For example, one can talk about motion of a wave or a quantum particle (or any other field) where the configuration consists of probabilities of occupying specific positions.
Uploaded
September 9th, 2013
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