Configuration space

In classical mechanics, the configuration space is the space of possible positions that a physical system may attain, possibly subject to external constraints. The configuration space of a typical system has the structure of a manifold; for this reason it is also called the configuration manifold.

Related Topics:
Classical mechanics - Physical system - Manifold

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For example, the configuration space of a single particle moving in ordinary Euclidean 3-space is just R3. For N particles the configuration space is R3N, or possibly the subspace where no two positions were equal. More generally, one can regard the configuration space of N particles moving in a manifold M as the function space MN.

Related Topics:
Euclidean 3-space - Function space

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To take account of both position and momenta one moves to the cotangent bundle of the configuration manifold. This larger manifold is called the phase space of the system. In short, a configuration space is typically "half" of (see Lagrangian distribution) a phase space that is constructed from a function space.

Related Topics:
Cotangent bundle - Phase space - Lagrangian distribution

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In quantum mechanics one formulation emphasises 'histories' as configurations.

Related Topics:
Quantum mechanics - Formulation

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Configuration spaces are related to braid theory, also, since the condition on a string of not passing through itself is formulated by cutting diagonals out of function spaces.

Related Topics:
Braid theory - Diagonal

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