Attitude Control of Flying Object using Gyroscopic Coupling

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Discussion Overview

The discussion focuses on the concept of attitude control of flying objects using gyroscopic coupling, particularly in the context of reaction wheels and gyroscopic precession. Participants explore the implications of gyroscopic effects on flight dynamics and control mechanisms, referencing technical equations and theories related to angular momentum.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on the term "gyroscopic coupling" as it appears in a technical report, questioning its relationship to angular velocity and precession.
  • Another participant suggests that "gyroscopic coupling" may refer to the effects of gyroscopic precession, providing an example from aviation where pilots must anticipate precession effects when controlling aircraft with rotary engines.
  • A different participant notes that helicopter pilots adjust their control inputs to compensate for gyroscopic precession, indicating a phase relationship between roll and pitch responses.
  • One participant expresses confusion about gyroscopic theory and requests resources for understanding forced precession and gyroscopic moments.
  • Another participant attempts to clarify their understanding of precession, discussing the relationship between angular momentum and torque, and suggesting that the inverse relationship should also be considered.
  • A later reply explains that the term arises from the need to express angular momentum in a rotating reference frame, introducing concepts like "inertial torque" and "Euler torque" as related terms.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and confusion regarding gyroscopic coupling and precession, with no consensus reached on the definitions or implications of these terms. Multiple perspectives on the topic are presented, indicating an ongoing exploration rather than a settled agreement.

Contextual Notes

Participants reference specific equations and concepts from a technical report, highlighting the complexity of the topic and the need for clarity in mathematical expressions. Some assumptions about the relationships between angular momentum, torque, and precession remain unaddressed.

eichfeld
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I am not really solving an exercise for homework so hopefully this general forum is OK for my question.

For my thesis, what is attitude control of a flying object with a reaction wheel, I am learning the basics from this NASA Technical Report:

http://www.hot.ee/ronn/design_glob_anal_ spacecraft _att_control.pdf (I mirrored it because currently NASA website publishing this is down)

Things are quite clear to me until eq (22) in PDF page 20, where the 3rd term is "gyroscopic coupling". I am unfamiliar with this phenomenon and can not grasp it from the equation. Could someone please explain me the meaning of this term? I do not see how can change of angular velocity depend only in the current velocity. Is it somehow the same thing as precession?
 
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eichfeld said:
Things are quite clear to me until eq (22) in PDF page 20, where the 3rd term is "gyroscopic coupling". [...] Is it somehow the same thing as precession?

I did some googling, and I did get the impression is that the expression 'gyroscopic coupling' is used for the case of experiencing consequences of gyroscopic precession.

If so then the most extreme example of gyroscopic coupling was the flight behavior of aircrafts with a single rotatory engine. With a rotatory engine the cylinders are arranged radially, and the entire motorblock is rotating. That was good for cooling the cilinders, but it was a huge rotating mass in a relatively light aircraft. If the pilot tried to pitch up or down, the aircraft wouldn't pitch but yaw, and vice versa. To fly those aircrafts the pilot's had to anticipate the gyroscopic precession and compensate for it in advance.

Cleonis
 
For a helicopter, the pilots control inputs are moved about 90 degrees out of phase, to compensate for gyroscopic precession. A roll torque results in a pitch response and vice versa. Yaw isn't an an issue since it shares an axis with the main rotor.
 
Hi, guys, sorry for the side orientated question,
but i am also confused exploring the gyroscope theory.
Could someone point out a web link with easy to understand explanations
of gyro basics, in particular forced precession equations and gyroscopic moment.

regards
 
Ok. I seem to understand what the term is. So in this case the Wa is velocity of precession, h is the moment of impuls percessing and the product without inertia term is the torque of precession?

Usually in textbooks they explain precession by applying torque to L and getting W from it, but it should also vice-versa, right?
 
eichfeld said:
Ok. I seem to understand what the term is. So in this case the Wa is velocity of precession, h is the moment of impuls percessing and the product without inertia term is the torque of precession?

Usually in textbooks they explain precession by applying torque to L and getting W from it, but it should also vice-versa, right?

What is your question? What you wrote is not clear enough.

Preferably, if your question is about a mathematical formula, enter the formula in LaTeX markup.
Check out the https://www.physicsforums.com/misc/howtolatex.pdf"

Cleonis
 
Last edited by a moderator:
This term arises because angular momentum is expressed in the body frame. This is of course a rotating reference frame, so the rotational equations of motion need to reflect this fact. Other names for this term include "inertial torque" (c.f. "inertial force", the fictitious forces due to frame acceleration/rotation) and "Euler torque" (c.f. the terms in Euler's equations).

An easy way to see how this term arises is to use the identity that relates the time derivative of a vector quantity q as ascertained from the perspective of an inertial frame versus a rotating frame:

\left(\frac {d\mathbf q}{dt}\right)_{\text{inertial}} =<br /> \left(\frac {d\mathbf q}{dt}\right)_{\text{rotating}} +\,\,<br /> \boldsymbol{\omega}\times \mathbf q

This is true for all vector quantities, not just position. So, apply it to angular momentum.

\left(\frac {d\mathbf L}{dt}\right)_{\text{rotating}} =<br /> \left(\frac {d\mathbf L}{dt}\right)_{\text{inertial}} -\,\,<br /> \boldsymbol{\omega}\times \mathbf L

The first term on the left hand side is simply the external torque. The second term is gyroscopic / inertial / Euler torque.
 

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