Place (physics)

The location is the position of a point or a body in spatial space . In addition to speed and acceleration , it is one of the central physical quantities of kinematics , a sub-area of mechanics . The location is represented by the location vector with the symbol or , the unit of which is the unit of length (usually: meter ). In the case of straight movements, scalar names are used e.g. B. used. The amount of the position vector is the distance between the point and the origin of the coordinates. Its components depend on the choice of the coordinate system . ${\ displaystyle {\ vec {r}}}$ ${\ displaystyle {\ vec {x}}}$ ${\ displaystyle x}$

If you consider the movement of a mass point or a body , then the location is a function of time:

{\ displaystyle {\ vec {r}} = {\ vec {r}} (t)}

This function is also called a trajectory or trajectory.

The first derivative of the location with respect to time gives the speed , the second derivative the acceleration : ${\ displaystyle {\ vec {v}}}$ ${\ displaystyle {\ vec {a}}}$

{\ displaystyle {\ vec {v}} (t) = {\ dot {\ vec {r}}} (t) = {\ frac {\ mathrm {d} {\ vec {r}} (t)} { \ mathrm {d} t}}}

{\ displaystyle {\ vec {a}} (t) = {\ dot {\ vec {v}}} (t) = {\ ddot {\ vec {r}}} (t) = {\ frac {\ mathrm {d} ^ {2} {\ vec {r}} (t)} {\ mathrm {d} t ^ {2}}}}

A mass point usually has three degrees of freedom of location, unless its movement is restricted by one or more constraints . Therefore, the location is clearly defined by specifying three coordinates - corresponding to the three spatial dimensions.

In the case of medium size scales, the location can be measured by direct measurement, in that the three components of the location vector are determined by comparison with suitable scales. For more distant objects, the location measurement usually results in a combination of direction and distance measurements , such as B. for radar or sonar measurements. The point of view of the observer is usually chosen as the origin of the coordinates.

In quantum mechanics , the location of a particle is an observable . As a result, the location is assigned its own operator , the location operator . Here the position measurement - together with the momentum measurement - is subject to Heisenberg's uncertainty relation .

Individual evidence

^ Paul A. Tipler, Gene Mosca: Physics: for scientists and engineers . 7th edition. Springer, 2015, ISBN 978-3-642-54165-0 . ( limited preview in Google Book search)
↑ Rolf Mahnken: Textbook of Technical Mechanics - Dynamics: A Descriptive Introduction . 2nd Edition. Springer, 2012, ISBN 978-3-642-19837-3 , pp. 9 . ( limited preview in Google Book search)

[1] Paul A. Tipler, Gene Mosca: Physics: for scientists and engineers . 7th edition. Springer, 2015, ISBN 978-3-642-54165-0 . ( limited preview in Google Book search)

[2] Rolf Mahnken: Textbook of Technical Mechanics - Dynamics: A Descriptive Introduction . 2nd Edition. Springer, 2012, ISBN 978-3-642-19837-3 , pp. 9 . ( limited preview in Google Book search)