The moment of inertia tensor | Chapter 25 Classical Mechanics 2

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2 жыл бұрын

Here we derive the form of the moment of inertia tensor and introduce its eigensystem. The eigenvectors are called the principal axes and the eigenvalues are called principal moments.
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Пікірлер: 16

@abhinav_mzn Жыл бұрын

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@boss_man9142 28 күн бұрын

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@davidvalero3075 2 жыл бұрын

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@wesleyblack8302 Жыл бұрын

4:20 what's the logic of relating a change in momentum to a constant velocity? instead either both a changing velocity and mass or the traditional change in velocity

@eastofthegreenline3324 Жыл бұрын

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@hans5259 11 ай бұрын

4:20 The cross product of 2 perpendicular vectors produces a new vector which is also perpendicular to the 2 previous vectors. does that mean vector ω has the same direction as vector L?

@Eye-vp5de 8 ай бұрын

Yes, the vectors are colinear, at least for the point particle

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@BRYDN_NATHAN 9 ай бұрын

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@omidoveisi1654 Жыл бұрын

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@lq_12 8 ай бұрын

I am not native english speaker. What do off diagonal elements mean??

@affafjunaid3814 5 ай бұрын

The elements inside a square matrix that do not lie on the main diagonal are called off-diagonal terms. If you write down a square matrix on a piece of paper, and draw a line through the matrix connecting the top left corner to the bottom right corner, all the elements that this line passes through are called diagonal elements. All the other elements are called off-diagonal elements. If you are familiar with matrix indices, then the diagonal elements are all those elements that have the same row and column number (i = j). And the off-diagonal elements are all those elements that have i not equal to j. Hope that clarifies 😊😊

@lq_12 5 ай бұрын

@@affafjunaid3814 Sorry 😔😔😔, that's the reason I clarified I am not a native English speaker. In the context of the inertia tensor what does non diagonal elements mean or say? Btw, thank you for the answer I liked it

@StevenDenenberg 4 ай бұрын

The inertia tensor is specific to a selection of axes. If all of the non-diagonal elements are zero, then the tensor is for the *principal* axes of the body. If the axes are principal axes, then a torque around an axis will only cause an acceleration of the angular velocity in *that* axis. If the non-diagonal tensor elements are not zero, then the axes of that tensor are not principal axes, and a torque around one axis can cause an acceleration of the angular velocity in a *different* axis!@@lq_12