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    ellipsoid of inertia

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    تاريخ التسجيل : 05/04/2008

    m14 ellipsoid of inertia

    مُساهمة من طرف teacher في الأربعاء 18 يونيو 2008, 7:44 pm

    Ellipsoid of Inertia

    The moments and products of inertia shown in [7] and [8] are basically specific to the local reference frame defined and reflect the mass distribution within the body in relation to the local reference frame. As shown in [6], the actual moment of inertia of a rigid body about an axis of rotation is a function of not only the moments and products of inertia for a given reference frame but also the orientation of the axis of rotation, a, b & g. Thus, it would be more accurate to say that the moment of inertia of a rigid body reflects the mass distribution within the body with respect to the axis of rotation.
    As the axis of rotation changes, so does the moment of inertia. To show this point clearly, let
    [9]
    Substituting [9] into [6] yields
    [10]
    Interestingly, [10] suffices the general form of the ellipsoid with its center at the origin of the reference frame. When Ixy = Iyz = Izx = 0, the ellipsoid defined by [10] definitely becomes symmetric about the three axes.
    Since
    [11]
    the distance from the center of the ellipsoid to the surface is 1 divided by the square root of the moment of inertia of the rigid body for a given orientation, a, b & g. The ellipsoid defined by [10] is called the ellipsoid of inertia since it describes the moment of inertia of an object as a function of the orientation of the axis of rotation.


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      الوقت/التاريخ الآن هو السبت 19 يناير 2019, 12:50 pm