code: def _validate_coordinates(
      coordinates=None,
      speeds=None,
      check_duplicates=True,
      is_dynamicsymbols=True,
      u_auxiliary=None,
  ):
      """Validate the generalized coordinates and generalized speeds.
  
      Parameters
      ==========
      coordinates : iterable, optional
          Generalized coordinates to be validated.
      speeds : iterable, optional
          Generalized speeds to be validated.
      check_duplicates : bool, optional
          Checks if there are duplicates in the generalized coordinates and
          generalized speeds. If so it will raise a ValueError. The default is
          True.
      is_dynamicsymbols : iterable, optional
          Checks if all the generalized coordinates and generalized speeds are
          dynamicsymbols. If any is not a dynamicsymbol, a ValueError will be
          raised. The default is True.
      u_auxiliary : iterable, optional
          Auxiliary generalized speeds to be validated.
  
      """
      t_set = {dynamicsymbols._t}
      # Convert input to iterables
      if coordinates is None:
          coordinates = []
      elif not iterable(coordinates):
          coordinates = [coordinates]
      if speeds is None:
          speeds = []
      elif not iterable(speeds):
          speeds = [speeds]
      if u_auxiliary is None:
          u_auxiliary = []
      elif not iterable(u_auxiliary):
          u_auxiliary = [u_auxiliary]
  
      msgs = []
      if check_duplicates:  # Check for duplicates
          seen = set()
          coord_duplicates = {
              x for x in coordinates if x in seen or seen.add(x)
          }
          seen = set()
          speed_duplicates = {
              x for x in speeds if x in seen or seen.add(x)
          }
          seen = set()
          aux_duplicates = {
              x for x in u_auxiliary if x in seen or seen.add(x)
          }
          overlap_coords = set(coordinates).intersection(speeds)
          overlap_aux = (
              set(coordinates).union(speeds).intersection(u_auxiliary)
          )
          if coord_duplicates:
              msgs.append(
                  f"The generalized coordinates {coord_duplicates} are "
                  f"duplicated, all generalized coordinates should be "
                  f"unique."
              )
          if speed_duplicates:
              msgs.append(
                  f"The generalized speeds {speed_duplicates} are "
                  f"duplicated, all generalized speeds should be unique."
              )
          if aux_duplicates:
              msgs.append(
                  f"The auxiliary speeds {aux_duplicates} are duplicated,"
                  f" all auxiliary speeds should be unique."
              )
          if overlap_coords:
              msgs.append(
                  f"{overlap_coords} are defined as both generalized "
                  f"coordinates and generalized speeds."
              )
          if overlap_aux:
              msgs.append(
                  f"The auxiliary speeds {overlap_aux} are also defined "
                  f"as generalized coordinates or generalized speeds."
              )
      if (
          is_dynamicsymbols
      ):  # Check whether all coordinates are dynamicsymbols
          for coordinate in coordinates:
              if not (
                  isinstance(coordinate, (AppliedUndef, Derivative))
                  and coordinate.free_symbols == t_set
              ):
                  msgs.append(
                      f'Generalized coordinate "{coordinate}" is not a '
                      f"dynamicsymbol."
                  )
          for speed in speeds:
              if not (
                  isinstance(speed, (AppliedUndef, Derivative))
                  and speed.free_symbols == t_set
              ):
                  msgs.append(
                      f'Generalized speed "{speed}" is not a dynamicsymbol.'
                  )
          for aux in u_auxiliary:
              if not (
                  isinstance(aux, (AppliedUndef, Derivative))
                  and aux.free_symbols == t_set
              ):
                  msgs.append(
                      f'Auxiliary speed "{aux}" is not a dynamicsymbol.'
                  )
      if msgs:
          raise ValueError("\n".join(msgs))
  
imports: from sympy.utilities import dict_merge
  from sympy.utilities.iterables import iterable
  from sympy.physics.vector import Dyadic, Vector, ReferenceFrame, Point, dynamicsymbols
  from sympy.physics.vector.printing import vprint, vsprint, vpprint, vlatex, init_vprinting
  from sympy.physics.mechanics.particle import Particle
  from sympy.physics.mechanics.rigidbody import RigidBody
  from sympy.simplify.simplify import simplify
  from sympy import Matrix, Mul, Derivative, sin, cos, tan, S
  from sympy.core.function import AppliedUndef
  from sympy.physics.mechanics.inertia import inertia, inertia_of_point_mass
  from sympy.utilities.exceptions import sympy_deprecation_warning
label_desc: Use image node_id 19 for calling a global function with example usage: _validate_coordinates(coordinates, speeds, check_duplicates, is_dynamicsymbols, u_auxiliary) without return types