
    sg              	       r    d dl mZ d dlmZmZmZmZ d dlmZ g dZ	ddZ
d Z G d d edd	d
g            Zy)    )sympify)PointDyadicReferenceFrameouter)
namedtuple)inertiainertia_of_point_massInertiac                 B   t        | t              st        d      t        |      t        |      t        |      }}}t        |      t        |      t        |      }}}|t	        | j
                  | j
                        z  |t	        | j
                  | j                        z  z   |t	        | j
                  | j                        z  z   |t	        | j                  | j
                        z  z   |t	        | j                  | j                        z  z   |t	        | j                  | j                        z  z   |t	        | j                  | j
                        z  z   |t	        | j                  | j                        z  z   |t	        | j                  | j                        z  z   S )a~  Simple way to create inertia Dyadic object.

    Explanation
    ===========

    Creates an inertia Dyadic based on the given tensor values and a body-fixed
    reference frame.

    Parameters
    ==========

    frame : ReferenceFrame
        The frame the inertia is defined in.
    ixx : Sympifyable
        The xx element in the inertia dyadic.
    iyy : Sympifyable
        The yy element in the inertia dyadic.
    izz : Sympifyable
        The zz element in the inertia dyadic.
    ixy : Sympifyable
        The xy element in the inertia dyadic.
    iyz : Sympifyable
        The yz element in the inertia dyadic.
    izx : Sympifyable
        The zx element in the inertia dyadic.

    Examples
    ========

    >>> from sympy.physics.mechanics import ReferenceFrame, inertia
    >>> N = ReferenceFrame('N')
    >>> inertia(N, 1, 2, 3)
    (N.x|N.x) + 2*(N.y|N.y) + 3*(N.z|N.z)

    z%Need to define the inertia in a frame)
isinstancer   	TypeErrorr   r   xyz)frameixxiyyizzixyiyzizxs          R/var/www/html/venv/lib/python3.12/site-packages/sympy/physics/mechanics/inertia.pyr	   r	      sO   J e^,?@@CL'#,cCCL'#,cCegguww''#eEGGUWW.E*EEegguww''(*-eEGGUWW.E*EFegguww''(*-eEGGUWW.E*EF egguww''( +.eEGGUWW.E*EF egguww''	( )    c                 
   | t        |j                  |j                        t        |j                  |j                        z   t        |j                  |j                        z   |j	                  |      z  t        ||      z
  z  S )aO  Inertia dyadic of a point mass relative to point O.

    Parameters
    ==========

    mass : Sympifyable
        Mass of the point mass
    pos_vec : Vector
        Position from point O to point mass
    frame : ReferenceFrame
        Reference frame to express the dyadic in

    Examples
    ========

    >>> from sympy import symbols
    >>> from sympy.physics.mechanics import ReferenceFrame, inertia_of_point_mass
    >>> N = ReferenceFrame('N')
    >>> r, m = symbols('r m')
    >>> px = r * N.x
    >>> inertia_of_point_mass(m, px, N)
    m*r**2*(N.y|N.y) + m*r**2*(N.z|N.z)

    )r   r   r   r   dot)masspos_vecr   s      r   r
   r
   8   su    4 	uww	 	uww	 
!	uww	 
! 
W		 "'w!8	9: :r   c                   L     e Zd ZdZ fdZe	 	 dd       Zd Zd ZeZ	eZ
 xZS )r   ay  Inertia object consisting of a Dyadic and a Point of reference.

    Explanation
    ===========

    This is a simple class to store the Point and Dyadic, belonging to an
    inertia.

    Attributes
    ==========

    dyadic : Dyadic
        The dyadic of the inertia.
    point : Point
        The reference point of the inertia.

    Examples
    ========

    >>> from sympy.physics.mechanics import ReferenceFrame, Point, Inertia
    >>> N = ReferenceFrame('N')
    >>> Po = Point('Po')
    >>> Inertia(N.x.outer(N.x) + N.y.outer(N.y) + N.z.outer(N.z), Po)
    ((N.x|N.x) + (N.y|N.y) + (N.z|N.z), Po)

    In the example above the Dyadic was created manually, one can however also
    use the ``inertia`` function for this or the class method ``from_tensor`` as
    shown below.

    >>> Inertia.from_inertia_scalars(Po, N, 1, 1, 1)
    ((N.x|N.x) + (N.y|N.y) + (N.z|N.z), Po)

    c                     t        |t              rt        |t              r||}}t        |t              st        d      t        |t              st        d      t        |   | ||      S )Nz'Reference point should be of type Pointz-Inertia value should be expressed as a Dyadic)r   r   r   r   super__new__)clsdyadicpoint	__class__s      r   r"   zInertia.__new__{   s^    fe$E6)B"E6E%'EFF&&)KLLwsFE22r   c	                 2     | t        |||||||      |      S )a  Simple way to create an Inertia object based on the tensor values.

        Explanation
        ===========

        This class method uses the :func`~.inertia` to create the Dyadic based
        on the tensor values.

        Parameters
        ==========

        point : Point
            The reference point of the inertia.
        frame : ReferenceFrame
            The frame the inertia is defined in.
        ixx : Sympifyable
            The xx element in the inertia dyadic.
        iyy : Sympifyable
            The yy element in the inertia dyadic.
        izz : Sympifyable
            The zz element in the inertia dyadic.
        ixy : Sympifyable
            The xy element in the inertia dyadic.
        iyz : Sympifyable
            The yz element in the inertia dyadic.
        izx : Sympifyable
            The zx element in the inertia dyadic.

        Examples
        ========

        >>> from sympy import symbols
        >>> from sympy.physics.mechanics import ReferenceFrame, Point, Inertia
        >>> ixx, iyy, izz, ixy, iyz, izx = symbols('ixx iyy izz ixy iyz izx')
        >>> N = ReferenceFrame('N')
        >>> P = Point('P')
        >>> I = Inertia.from_inertia_scalars(P, N, ixx, iyy, izz, ixy, iyz, izx)

        The tensor values can easily be seen when converting the dyadic to a
        matrix.

        >>> I.dyadic.to_matrix(N)
        Matrix([
        [ixx, ixy, izx],
        [ixy, iyy, iyz],
        [izx, iyz, izz]])

        )r	   )	r#   r%   r   r   r   r   r   r   r   s	            r   from_inertia_scalarszInertia.from_inertia_scalars   s#    f 75#sCc3?GGr   c                 v    t        d| j                  j                   d|j                  j                   d      )Nz$unsupported operand type(s) for +: '' and ''r   r&   __name__selfothers     r   __add__zInertia.__add__   @      NN334 5!OO445Q8 9 	9r   c                 v    t        d| j                  j                   d|j                  j                   d      )Nz$unsupported operand type(s) for *: 'r*   r+   r,   r.   s     r   __mul__zInertia.__mul__   r2   r   r   r   r   )r-   
__module____qualname____doc__r"   classmethodr(   r1   r4   __radd____rmul____classcell__)r&   s   @r   r   r   Y   sA     B3 JK!"2H 2Hh9
9
 HHr   r   r$   r%   Nr5   )sympyr   sympy.physics.vectorr   r   r   r   collectionsr   __all__r	   r
   r    r   r   <module>rB      s<     E E "
9-)`:BljXw$78 lr   