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The mathematical description of motion, or kinematics, is based on the idea of specifying positions using numerical coordinates. Movement is represented by these numbers changing over time: a body's trajectory is represented by a function that assigns to each value of a time variable the values of all the position coordinates.
The number of independent coordinates is n = 3N − C. (In D dimensions, the original configuration would need ND coordinates, and the reduction by constraints means n = ND − C). It is ideal to use the minimum number of coordinates needed to define the configuration of the entire system, while taking advantage of the constraints on the system.
Angular speed and tangential speed on a disc Tangential speed is the speed of an object undergoing circular motion, i.e., moving along a circular path. [6] A point on the outside edge of a merry-go-round or turntable travels a greater distance in one complete rotation than a point nearer the center.
Displacement is the shift in location when an object in motion changes from one position to another. [2] For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity (a vector), whose magnitude is the average speed (a scalar quantity).
[5] [6] If is the initial position of an object and is the final position, then mathematically the displacement is given by: = The equivalent of displacement in rotational motion is the angular displacement measured in radians. The displacement of an object cannot be greater than the distance because it is also a distance but the shortest one.
The navigator plots their 9 a.m. position, indicated by the triangle, and, using their course and speed, estimates their own position at 9:30 and 10 a.m. In navigation , dead reckoning is the process of calculating the current position of a moving object by using a previously determined position, or fix , and incorporating estimates of speed ...
Fitts's law: draft of target size W and distance to target D. Fitts's law (often cited as Fitts' law) is a predictive model of human movement primarily used in human–computer interaction and ergonomics.
where x' is the position as seen by a reference frame that is moving at speed, v, in the "unprimed" (x) reference frame. [note 3] Taking the differential of the first of the two equations above, we have, ′ =, and what may seem like the obvious [note 4] statement that ′ =, we have: