def output_equations(x):
    """Returns the outputs of the system. For now just the an array of the
    generalized coordinates.

    Parameters
    ----------
    x : ndarray, shape(N, n)
        The trajectories of the system states.

    Returns
    -------
    y : ndarray, shape(N, o)
        The trajectories of the generalized coordinates.

    Notes
    -----
    The order of the states is assumed to be:

    [coord_1, ..., coord_{n/2}, speed_1, ..., speed_{n/2}]

    [q_1, ..., q_{n/2}, u_1, ...., u_{n/2}]

    As this is what generate_ode_function creates.

    """
    return x[:, :x.shape[1] // 2]
