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MappingBetweenLocalAndGlobalCoordinateIndices.rst

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Mapping between local and global coordinate indices

The :ref:`LTG <LTG>`-index-mappings(local-to-global coordinate index mappings containing transformation from local object coordinate indices to global (system) coordinate indices; this is different for coordinate transformations!) between local coordinate indices, on node or object level, and global (=system) coordinate indices follows the following rules:

  • :ref:`LTG <LTG>`-index-mappings are computed during mbs.Assemble() and are not available before.
  • Nodes own a global index which relates the local coordinates to global (system) coordinate. E.g., for a :ref:`ODE2 <ODE2>` node with node number i, this index can be obtained via the function mbs.GetNodeODE2Index(i).
  • The order of global coordinates is simply following the node numbering. If we add three nodes NodePoint, the system will contain 9 coordinates, where the first triple (starting index 0) belongs to node 0, the second triple (starting index 3) belongs to node 1 and the third triple (starting index 6) belongs to node 2. After mbs.Assemble(), you can access the system coordinates via mbs.systemData.GetODE2Coordinates(), which returns a numpy array with 9 coordinates, containing the initial values provided in NodePoint (default: zero).
  • Objects have their own :ref:`LTG <LTG>`-index-mappings for their respective coordinate types. The :ref:`ODE2 <ODE2>` coordinates of an object j can be retrieved via mbs.systemData.GetObjectLTGODE2(j). For a body, these are the global :ref:`ODE2 <ODE2>` coordinates representing the body; for a connector, these are the coordinates to which the connector is linked (usually coordinates of two bodies); for a ground object, the :ref:`LTG <LTG>`-index-mapping is empty; see also Section :ref:`sec-systemdata-objectltg`.
  • Constraints create algebraic variables (Lagrange multipliers) automatically. For a constraint with object number k, the global index to algebraic variables (of :ref:`AE <AE>`-type) can be accessed via mbs.systemData.GetObjectLTGAE(k).