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Space. Space is a three-dimensional continuum containing positions and directions. [1] In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. [2]
Space physics, also known as space plasma physics, is the study of naturally occurring plasmas within Earth's upper atmosphere and the rest of the Solar System. It includes the topics of aeronomy, aurorae, planetary ionospheres and magnetospheres, radiation belts, and space weather (collectively known as solar-terrestrial physics [1] ).
t. e. In dynamical systems theory and control theory, a phase space or state space is a space in which all possible "states" of a dynamical system or a control system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of ...
t. e. In physics, spacetime is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects such as how different observers perceive where and when events occur.
The three-dimensional linear vector space R3 is a set of all radius vectors. The space R3 is endowed with a scalar product , . Time is a scalar which is the same in all space E3 and is denoted as t. The ordered set { t } is called a time axis. Motion (also path or trajectory) is a function r : Δ → R3 that maps a point in the interval Δ from ...
Its configuration space is the subset of coordinates in that define points on the sphere . In this case, one says that the manifold is the sphere, i.e. . For n disconnected, non-interacting point particles, the configuration space is . In general, however, one is interested in the case where the particles interact: for example, they are ...
In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points. The distance is measured by a function called a metric or distance function. [1] Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry .
Motivating example: Euclidean vector space. One of the most familiar examples of a Hilbert space is the Euclidean vector space consisting of three-dimensional vectors, denoted by R 3, and equipped with the dot product. The dot product takes two vectors x and y, and produces a real number x ⋅ y.