basic_tools:configuration_space
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basic_tools:configuration_space [2018/05/05 11:51] jakobadmin ↷ Links adapted because of a move operation |
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| [{{ :basic_tools:pendulumconfiguspace.png?nolink&300|Configuration space of a double pendulum. [[http://math.ucr.edu/home/baez/classical/texfiles/2005/book/classical.pdf|Source]]}}] | [{{ :basic_tools:pendulumconfiguspace.png?nolink&300|Configuration space of a double pendulum. [[http://math.ucr.edu/home/baez/classical/texfiles/2005/book/classical.pdf|Source]]}}] | ||
| - | Another good example is the [[models:basis_models:pendulum|pendulum]]. The total configuration space of a pendulum swinging just in two dimensions is a circle $S^1$, since a pendulum can swing once around its suspension. The configuration space of a pendulum swinging in 3-dimensions is the sphere $S^2$. | + | Another good example is the [[models:basic_models:pendulum|pendulum]]. The total configuration space of a pendulum swinging just in two dimensions is a circle $S^1$, since a pendulum can swing once around its suspension. The configuration space of a pendulum swinging in 3-dimensions is the sphere $S^2$. |
| This is useful, since now we can describe our system in terms of paths in the configuration space. The system starts in one specific configuration, which corresponds to one point in the configuration space. Then as it evolves this point starts moving around in configuration space. Thus, we only need to keep track of how this one point moves around. | This is useful, since now we can describe our system in terms of paths in the configuration space. The system starts in one specific configuration, which corresponds to one point in the configuration space. Then as it evolves this point starts moving around in configuration space. Thus, we only need to keep track of how this one point moves around. | ||
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| <tabbox Why is it interesting?> | <tabbox Why is it interesting?> | ||
| - | In the [[formalisms:lagrangian_formalism|Lagrangian formalism]], we describe what happens in [[theories:classical_mechanics:newtonian_mechanics|classical mechanics]] by referring to points in the configuration space. In this sense, the configuration space is for the Lagrangian formalism, what the phase space is for the [[formalisms:hamiltonian_formalism|Hamiltonian formalism]]. | + | In the [[formalisms:lagrangian_formalism|Lagrangian formalism]], we describe what happens in [[theories:classical_mechanics:newtonian|classical mechanics]] by referring to points in the configuration space. In this sense, the configuration space is for the Lagrangian formalism, what the phase space is for the [[formalisms:hamiltonian_formalism|Hamiltonian formalism]]. |
| Configuration spaces are also the central objects in robotics, as the set of reachable positions by a robot. | Configuration spaces are also the central objects in robotics, as the set of reachable positions by a robot. | ||
basic_tools/configuration_space.txt · Last modified: 2020/01/08 11:05 by jakobadmin
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