(frame, *body)
return kinetic_energy(frame, *body) - potential_energy(*body)
Lagrangian of a multibody system.

    This function returns the Lagrangian of a system of Particle's and/or
    RigidBody's. The Lagrangian of such a system is equal to the difference
    between the kinetic energies and potential energies of its constituents. If
    T and V are the kinetic and potential energies of a system then it's
    Lagrangian, L, is defined as

    L = T - V

    The Lagrangian is a scalar.

    Parameters
    ==========

    frame : ReferenceFrame
        The frame in which the velocity or angular velocity of the body is
        defined to determine the kinetic energy.

    body1, body2, body3... : Particle and/or RigidBody
        The body (or bodies) whose Lagrangian is required.

    Examples
    ========

    >>> from sympy.physics.mechanics import Point, Particle, ReferenceFrame
    >>> from sympy.physics.mechanics import RigidBody, outer, Lagrangian
    >>> from sympy import symbols
    >>> M, m, g, h = symbols('M m g h')
    >>> N = ReferenceFrame('N')
    >>> O = Point('O')
    >>> O.set_vel(N, 0 * N.x)
    >>> P = O.locatenew('P', 1 * N.x)
    >>> P.set_vel(N, 10 * N.x)
    >>> Pa = Particle('Pa', P, 1)
    >>> Ac = O.locatenew('Ac', 2 * N.y)
    >>> Ac.set_vel(N, 5 * N.y)
    >>> a = ReferenceFrame('a')
    >>> a.set_ang_vel(N, 10 * N.z)
    >>> I = outer(N.z, N.z)
    >>> A = RigidBody('A', Ac, a, 20, (I, Ac))
    >>> Pa.set_potential_energy(m * g * h)
    >>> A.set_potential_energy(M * g * h)
    >>> Lagrangian(N, Pa, A)
    -M*g*h - g*h*m + 350
Lagrangian of a multibody system.
Lagrangian of a multibody system .
def Lagrangian(frame, *body):
    """Lagrangian of a multibody system.

    This function returns the Lagrangian of a system of Particle's and/or
    RigidBody's. The Lagrangian of such a system is equal to the difference
    between the kinetic energies and potential energies of its constituents. If
    T and V are the kinetic and potential energies of a system then it's
    Lagrangian, L, is defined as

    L = T - V

    The Lagrangian is a scalar.

    Parameters
    ==========

    frame : ReferenceFrame
        The frame in which the velocity or angular velocity of the body is
        defined to determine the kinetic energy.

    body1, body2, body3... : Particle and/or RigidBody
        The body (or bodies) whose Lagrangian is required.

    Examples
    ========

    >>> from sympy.physics.mechanics import Point, Particle, ReferenceFrame
    >>> from sympy.physics.mechanics import RigidBody, outer, Lagrangian
    >>> from sympy import symbols
    >>> M, m, g, h = symbols('M m g h')
    >>> N = ReferenceFrame('N')
    >>> O = Point('O')
    >>> O.set_vel(N, 0 * N.x)
    >>> P = O.locatenew('P', 1 * N.x)
    >>> P.set_vel(N, 10 * N.x)
    >>> Pa = Particle('Pa', P, 1)
    >>> Ac = O.locatenew('Ac', 2 * N.y)
    >>> Ac.set_vel(N, 5 * N.y)
    >>> a = ReferenceFrame('a')
    >>> a.set_ang_vel(N, 10 * N.z)
    >>> I = outer(N.z, N.z)
    >>> A = RigidBody('A', Ac, a, 20, (I, Ac))
    >>> Pa.set_potential_energy(m * g * h)
    >>> A.set_potential_energy(M * g * h)
    >>> Lagrangian(N, Pa, A)
    -M*g*h - g*h*m + 350

    """

    if not isinstance(frame, ReferenceFrame):
        raise TypeError('Please supply a valid ReferenceFrame')
    for e in body:
        if not isinstance(e, (RigidBody, Particle)):
            raise TypeError('*body must have only Particle or RigidBody')
    return kinetic_energy(frame, *body) - potential_energy(*body)
def Lagrangian ( frame , * body ) : if not isinstance ( frame , ReferenceFrame ) : raise TypeError ( 'Please supply a valid ReferenceFrame' ) for e in body : if not isinstance ( e , ( RigidBody , Particle ) ) : raise TypeError ( '*body must have only Particle or RigidBody' ) return kinetic_energy ( frame , * body ) - potential_energy ( * body )