Mass

[Peter230655]

1. The step from eq(100) to eq(101), with eq(97) is not obvious to me, I am not familiar how to calculate terms like a.dot(b.cross(c)). Am I overlooking something obvious? Otherwise maybe you could give the rule, or add a link to where the rules may be. (I did not find anything good..)

2. In eq(100), you write

I_ab := I_hat_a . N_hat_b

I think, this I_hat should be I_dash, a typo?

3. Dyadics Would it make sense, to stress a bit more that these terms

outer(A.x. A.y), etc

play the role of units in the dyadics, just like the n_hat do with vectors. You mention it in passing, of course.

4. Inertia Dyadic I used the vector triple product identity to calculate eq(100) (for one term of the sum only), with obvious abbreviations:

[r x (n_a x r)] . n_b = [n_a(r . r) - r(r . n_a)] . n_b = -(r . n_b) . (r . n_a)

but it did not help me with eq(101)

[moorepants]

Am I overlooking something obvious?

I'm using the definition of the cross product. |a x b| = |a||b|sin(\theta)

I think, this I_hat should be I_dash, a typo?

Fixed

play the role of units in the dyadics, just like the n_hat do with vectors.

I added a bit more text about this.

I used the vector triple product identity to calculate eq(100) (for one term of the sum only), with obvious abbreviations:

I'm only using the single cross product magnitude and recognizing that na is a unit vector.

[Peter230655]

Below eq(23) you give some rules for the cross product.

Below eq(109), you give rules for dyadics. There you also give the rules for ‚combinations‘ of dot and diyadics / cross and dyadics, which make your calculations of eq(110) very clear.

Would it make sense to add such rules of ‚combinations‘ of dot and cross below eq(23) ?

On Tue 22. Mar 2022 at 04:40 Jason K. Moore @.***> wrote:

Am I overlooking something obvious?

I'm using the definition of the cross product. |a x b| = |a||b|sin(\theta)

I think, this I_hat should be I_dash, a typo?

Fixed

play the role of units in the dyadics, just like the n_hat do with vectors.

I added a bit more text about this.

I used the vector triple product identity to calculate eq(100) (for one term of the sum only), with obvious abbreviations:

I'm only using the single cross product magnitude and recognizing that na is a unit vector.

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-- Best regards,

Peter Stahlecker

[moorepants]

Would it make sense to add such rules of ‚combinations‘ of dot and cross below eq(23) ?

Yes, I can add more there. I can put the triple cross product there for sure. are there other rules?

[Peter230655]

Frankly, I do not know - it has been a long time…… I did not find anything decent in the internet, and I am in Bangladesh, far away from my books. Should there not be some rule for (a x b).dot(c) ? (This is what you calculated going from eq(100) to eq(101), using eq(97), except you did it from ‚first principles‘.)

I know, your lecture is not about math, but don’t engineering students normally like such formulae?

On Tue 22. Mar 2022 at 11:31 Jason K. Moore @.***> wrote:

Would it make sense to add such rules of ‚combinations‘ of dot and cross below eq(23) ?

Yes, I can add more there. I can put the triple cross product there for sure. are there other rules?

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-- Best regards,

Peter Stahlecker

[moorepants]

Should there not be some rule for (a x b).dot(c) ?

Yes, I just need to formulate which ones are missing/needed and add them.

[moorepants]

Closing in favor of #98.