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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.
basic_tools/configuration_space.1525513918.txt.gz · Last modified: 2018/05/05 09:51 (external edit)