- #1

Trying2Learn

- 375

- 57

Good Morning All.

I have asked this before, but my post was not clear (my fault: I apologize). I hope this is more clear (please be patient as I try to get to the core of my confusion).

In this case, the motions will adhere to Euler angles: 3-axis, then 1, then 3 again)

My question is a general one: upon seeing a spinning top for the first time, how did they decide which motion should be modeled first?

In other words, to demonstrate my stupidity, we apply the rotation matrices as:

PRECESSION MATRIX x NUTATION MATRIX x SPIN MATRIX

But I cannot seem to figure out how they decided they PRECESSION was the first one. I know that one cannot commute rotation matrices, but (and set aside the fact that the upper top is isomorphic to the gyro and set aside that one could use Tait angles) what made them decide on that order and not this order, just by looking at it:

NUTATION MATRIX x PRECESSION MATRIX x SPIN MATRIX

In other words... If I were to be so naive as to model the nutaiton first, then I would have no way to rotate the figure on the right, below, into a model for the precession. I can assume that the body spin is last. This is a lot of handwaving by me, and I am almost comfortable with it, but not really.

I have asked this before, but my post was not clear (my fault: I apologize). I hope this is more clear (please be patient as I try to get to the core of my confusion).

- In the first figure, below, the spinning top precesses as shown (well, it is not a animated jpg, but it should be clear by reading the text bos)
- In the second figure, the top nutates
- Finally, it spins.

In this case, the motions will adhere to Euler angles: 3-axis, then 1, then 3 again)

My question is a general one: upon seeing a spinning top for the first time, how did they decide which motion should be modeled first?

In other words, to demonstrate my stupidity, we apply the rotation matrices as:

PRECESSION MATRIX x NUTATION MATRIX x SPIN MATRIX

But I cannot seem to figure out how they decided they PRECESSION was the first one. I know that one cannot commute rotation matrices, but (and set aside the fact that the upper top is isomorphic to the gyro and set aside that one could use Tait angles) what made them decide on that order and not this order, just by looking at it:

NUTATION MATRIX x PRECESSION MATRIX x SPIN MATRIX

In other words... If I were to be so naive as to model the nutaiton first, then I would have no way to rotate the figure on the right, below, into a model for the precession. I can assume that the body spin is last. This is a lot of handwaving by me, and I am almost comfortable with it, but not really.

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