# Configuration Space

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The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Configuration Space

an n -dimensional space, with the number of dimensions equal to the number n of degrees of freedom of a system. It is used to arbitrarily represent the motion of the entire system as the motion of some point in this space.

When a mechanical system moves with respect to some frame of reference, its configuration, that is, the position of the system itself and the relative positions of its parts, can be determined at any moment of time by the generalized coordinates q1, q2. … , qn. If these coordinates are considered as n Cartesian coordinates in n -dimensional space, a definite point in this space, called the image point, will correspond to each configuration of the system. Such a space is called a configuration space. For example, in systems with one, two, or three degrees of freedom (for example, a plane mathematical pendulum, a spherical pendulum, or a free material point) the configuration space will be a line, plane, or three-dimensional space, respectively. For a free rigid body with six degrees of freedom, the configuration space will be six-dimensional.

The configuration of a moving system will continuously vary and the image point will also continuously vary its position in the configuration space, tracing a curve called by convention the trajectory of the system. Consequently, the motion of a system can be represented as the motion of the image point in the configuration space. Such a representation is used in the consideration of certain properties of a moving system, particularly properties established by a number of variational principles of mechanics.

S. M. TARG

References in periodicals archive ?
Recently, starting in [1], the topology of the configuration space of spatial polygons of arbitrary edge lengths has been considered by many authors.
The mathematical structure of realist quantum theories has given rise to a debate about how our ordinary three-dimensional space is related to the 3N-dimensional configuration space on which the wave function is defined.
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The representative statement of this motion planning problem is known as the configuration space formulation.
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Obviously, the roadmap cannot be too small or else it ceases to be useful, because it doesn't capture the connectivity of the configuration space.

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