In this frame, at least the moment of inertia tensor is constant ( and diagonal ), which simplifies calculations.
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The inertia tensor describes the location of each particle of mass in a given object in relation to the object's center of mass.
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:Classical mechanics, especially anything involving resonance, the moment of inertia tensor, etc . All this even more so in engineering applications.
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The angular velocity of a rigid body takes a Euler's rigid body equations are simpler because the inertia tensor is constant in that frame.
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Use of Cartesian tensors occurs in physics and engineering, such as with the Cauchy stress tensor and the moment of inertia tensor in rigid body dynamics.
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The angular kinetic energy may be expressed in terms of the moment of inertia tensor \ mathbf { I } and the angular velocity vector \ boldsymbol \ omega
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If we start blocking people for having the " exact same agenda, " we could start with you, Badagnani, Hypnosadist, Jehochman, and Inertia Tensor.
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When we apply this constraint, we diagonalize the moment of inertia tensor, which simplifies our three equations into a special set of equations called Euler's equations.
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The arms have inertia tensors \ boldsymbol { J } _ 1 and \ boldsymbol { J } _ 2 ( about the centre of mass of the arm ).
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Therefore, we change to a coordinate frame fixed in the rotating body, and chosen so that its axes are aligned with the principal axes of the moment of inertia tensor.
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