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basic_tools:configuration_space [2018/05/05 11:51] jakobadmin ↷ Links adapted because of a move operation |
basic_tools:configuration_space [2020/01/08 11:05] (current) jakobadmin [Intuitive] |
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Formulated differently, the configuration space is the possible "positions" of a mechanical system. Take note that the states of motion, eg. velocities/momenta are not part of the configuration space. This is in contrast to the [[basic_tools:phase_space|phase space]], where we also take the states of motion into account. | Formulated differently, the configuration space is the possible "positions" of a mechanical system. Take note that the states of motion, eg. velocities/momenta are not part of the configuration space. This is in contrast to the [[basic_tools:phase_space|phase space]], where we also take the states of motion into account. | ||
- | The state of a system is recorded in a configuration space point through all the locations and all the velocities that the objects in the system have at a given point in time. | + | The state of a system is recorded in a configuration space point through all the locations that the objects in the system have at a given point in time. |
The time evolution of a system can then be represented as a path in configuration space. | The time evolution of a system can then be represented as a path in configuration space. | ||
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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. |