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‫So what really happens if the body is not mass symmetric to see it, let's ride it out, we can write

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‫down the moment and then the body frame, angular acceleration relationship like this.

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‫And now we're just going to write out this entire system.

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‫If you do that, then this is what you will get.

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‫You can see that now you have a much more complicated system of equations.

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‫If you have a moment about the body frame, x axis, body frame, y axis and body frame Z axis, if

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‫you have these three moments here, there are not zero, then this entire system of equations becomes

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‫much more complicated.

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‫If you're a product of inertia or not zero, then you can see that part of your moment about the body

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‫frame x axis that you apply about the body frame x axis.

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‫It not only contributes to angular acceleration about the X axis, but this Mexican moment also contributes

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‫to angular acceleration about the body frame, Y and Z axis.

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‫And the same thing here this moment, m, y, y.

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‫Not only it contributes to this thing that it does anyway when all the products of inertia are zeros.

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‫But in addition to that, it also contributes to this p dot and our dot and the same thing here.

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‫Normally it contributes to this one, but it also contributes to this one and this one.

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‫So when all your products of inertia are non zeros and you have moments about all the three axis, then

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‫you have a situation where each moment contributes to angular accelerations about all the three axis.

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‫That obviously complicates the calculations.

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‫That is why engineers try to design things with mass symmetry.

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‫Then products of inertia become zeros and your inertia tensor becomes like this.

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‫This is much easier to deal with.

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‫And now, of course, that is what we will have.

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‫We will assume mass symmetry about all the axis.

25
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‫So you have a wave here.

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‫This is your body frame x axis, this is your body frame y axis and this is your body frame Z axis.

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‫And we assume mass symmetry about all these axis.

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‫So we will only deal with this matrix here.

29
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‫And by the way, one final remark about this topic is that if you achieve a situation where products

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‫of inertia are zero kilogram times meter squared, in other words, when you achieve this matrix and

31
00:03:07,890 --> 00:03:17,310
‫you only have to deal with these mass moments of inertia, then the axis about which these mass moments

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‫of inertia are calculated.

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00:03:19,890 --> 00:03:23,790
‫These axes are called principle axis.

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00:03:24,240 --> 00:03:29,360
‫So in the next video, we will start deriving fundamental dynamics equations.

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‫So see you there and thank you very much.