Position (Vector) Information
In geometry, a position, location, or radius vector, usually denoted , is a vector which represents the position of a point P in space in relation to an arbitrary reference origin O: . It corresponds to the displacement from O to P. The concept applies to two- or three-dimensional space.[1] The term is also used as a means of deriving displacement by the spatial comparison of two or more position vectors and are usually 2- or, through hyperspace-based theories, 3-dimensional or N-dimensional if belonging to an N-dimensional Euclidean hyperspace.[1]
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Applications
- In linear algebra, a position vector can be expressed as a linear combination of basis vectors.
- The kinematic movement of a point mass can be described by a vector-valued function giving the position as a function of the scalar time parameter t. These are used in mechanics and dynamics to keep track of the positions of particles, point masses, or rigid objects.
- In differential geometry, position vector fields are used to describe continuous and differentiable space curves, in which case the independent parameter need not be time, but can be (e.g.) arc length of the curve.
Derivatives of Position[2]
Velocity
Acceleration
Jolt/Jerk/Surge/Lurch
Snap/Jounce
Crackle/Trounce
Pop/Pounce
Where is the position vector, is the velocity vector, is the acceleration vector, is the jerk vector, is the snap vector, is the crackle vector, and is the pop vector.
Relationship to displacement vectors
A displacement vector can be defined as the action of uniformly translating spatial points in a given direction over a given distance. Thus the addition of displacement vectors expresses the composition of these displacement actions and scalar multiplication as scaling of the distance. With this in mind we may then define a position vector of a point in space as the displacement vector mapping a given origin to that point. Note thus position vectors depend on a choice of origin for the space, as well as displacement vectors depend on the choice of an initial point.
See also
Notes
- ^ a b Keller, F. J, Gettys, W. E. et al. (1993), p28-29
- ^ http://wearcam.org/absement/Derivatives_of_displacement.htm
References
- Keller, F. J, Gettys, W. E. et al. (1993). "Physics: Classical and modern" 2nd ed. McGraw Hill Publishing
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