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Gyroscopes for the linearly minded

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Dr. Slack

Sat Jan 24 2015, 03:38PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

Rather than continue on the IC engine generator thread, which was not about gyroscopes per se, I'll start a new thread for gyroscopes.

This treatment stems from a real experiment I did as a youth, and a number of thought experiments as a student. I was fascinated by gyroscopes. My aha moment was when I asked myself what was the centri-whatever tension in the string of a conker being whirled about an axis, and what was the period of a simple pendulum with the same length, same mass, and gravity equal to the tension in the string. It turns out to be identically the rotation period. This could not be a coincidence, and sure enough set me off thinking about free gyroscopes and their linear equivalents.

Anyhow, try this presentation for taste. Unfortunately it's not come out as convincingly as I'd like. It's correct technically, but I fear it may fall into the same trap of 'its only clear if you know what I'm talking about already'. I'd like your comments on whether it's persuasive or not, or helps anyone. I'm sure a video of something like this setup, but with 2 weights for mechanical symmetry, would be infinitely better than these line drawings.

Enjoy, try not to get confused

Andy

Sat Jan 24 2015, 05:20PM

Registered Member #4266 Joined: Fri Dec 16 2011, 03:15AM
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One

Hazmatt_(The Underdog)

Sat Jan 24 2015, 05:24PM

Registered Member #135 Joined: Sat Feb 11 2006, 12:06AM
Location: Anywhere is fine
Posts: 1735

In your last slide, when 3 vectors are perpindicular to each other, they are orthogonal.

4 years of Calculus, and I finally get to use the word Orthogonal... heheh.

Dr. Slack

Sat Jan 24 2015, 05:59PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

1.5, thanks

Andy

Sun Jan 25 2015, 07:10AM

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Two

Dr. Slack

Sun Jan 25 2015, 11:46AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

2.5, thanks

Ash Small

Mon Jan 26 2015, 12:51AM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

It's pretty good. I had to read it three times to fully follow it, even being familiar with the concept, and think it could be improved, but maybe I'd just have written it differently.

Personally, I think diagrams should be pretty self explanatory, and think 3D would be better, especially if you can 'toggle and rotate'. I've had a bit of experience with translucent 3D CGI, so may be able to assist if required.

It's precise and 'to the point'. When I do stuiff like this I try to edit it down to the fewest words possible.

EDIT: I think that word is either centrifugal or centripetal

Dr. Slack

Mon Jan 26 2015, 07:16AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

Ash Small wrote ...

EDIT: I think that word is either centrifugal or centripetal

This is not the thread for discussing centri-whatever force, this is the thread for trying to understand the initially counter-intuitive behaviour of gyroscopes by reference to linear mechancis.

But as we're here. it's one or the other, depending on whether you have a stationary or rotating frame of reference. Unfortunately using the correct one doesn't stop people misunderstanding and arguing, it's almost a religious emacs or vi thing! Which is why I'm not discussing it further. The string (in finest physics tradition, a light, inextensible string) whirling the nut is taut, and that's all we need to know.

Uspring

Mon Jan 26 2015, 01:36PM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
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Nice derivation. Actual gyros are rigid, though, which involves some complications. If you consider e.g. a rigid rotor made from two masses placed symmetrically opposite the rotational axis in order to avoid wiggle and then tilt the axis at constant rotational speed, the magnitude of the torque felt won't be exactly constant and also not the rotational speed around the rotor axis. For a rotationally symmetric rotor, they will be constant. Entirely non obvious and I needed to solve the Lagrangian for the system to see that.

Dr. Slack

Mon Jan 26 2015, 03:06PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

What I didn't add to the presentation, though I'm sort of hoping the connection will be made by readers, is that a typical gyroscope wheel is 'simply' a large number of nuts all being whirled round, spread out around the rim. The torque is then applied to the rim through the bearings, axle and wheel, rather than by air jets externally. I think applying the torque as an impulse as I did is the ultimate in non-constant torques.

The main idea was to show that the precession has nothing to do with there physically being a wheel or axle, just the chosen frame of reference together with linear mechanics is sufficient for particles on the rim.

I had a Lagrangian once, but changed to a Volvo for the better load capacity.

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