Mindscrape, I've sent you a visitor message. I suggest, very hopefully and without any sort of proof, the following hypothetical theorem:
Let S be the set of all 3D shapes which have at least a uniform cross-section on one axis and/or some degree of symmetry?.
Let T be the set SxMxC where M is...
No, my excitement above must be mis-placed. If the object is rotated with respect to the axes - no. If both axes and object are rotated - yes. But that's pretty useless. I'm going to have to study tensors.
Mike
Thanks a million, Mindscrape. I had derived something like your second integral above. The problem is there are a large number of terms in the solution and so it is not suitable for use as a primitive. So a method of approximation seems to be the best way.
What I want to do is to find an...
Mindscrape, thank you very much for your comment. My fundamental problem is that I am very isolated, millions of miles from anywhere. Do you know of a free course of Vectors and Tensors on Internet that would help me to understand your solution? Failing that, a good shortbook from Amazon?
My...
Perhaps Tensor Calculus holds the answer; but I just can't justify the time for studying that as I know nothing of it.
The end objective is to calculate the mass moment of inertia of the yellow solid parallelepiped about rectangular axes through its centre of mass as in the diagram here...