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4hv.org :: Forums :: General Science and Electronics
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Need Help Related to Rotational Inertia

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BigBad
Tue Mar 19 2013, 05:51PM
BigBad Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
Location:
Posts: 600
You could do that, but you don't have to use Lagrangian at all, you can just use step-wise integration, it's actually very simple. Provided you make the steps small enough it usually works very well indeed.

Stuff like:

ds = vt +0.5 * a * dt^2
dv = a * dt
a = F/m

and a few simple equations for the rotation

those get you an awful long way with dt small
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WaveRider
Tue Mar 19 2013, 08:19PM
WaveRider Registered Member #29 Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500
BigBad wrote ...

You could do that, but you don't have to use Lagrangian at all, you can just use step-wise integration, it's actually very simple. Provided you make the steps small enough it usually works very well indeed.

Stuff like:

ds = vt +0.5 * a * dt^2
dv = a * dt
a = F/m

and a few simple equations for the rotation

those get you an awful long way with dt small

mistrust
OK smartypants, why don't you write out the system of equations we need to solve for two coupled rotors, airframe, body forces/torques and PID flight control system, post them here and save us all the trouble. Then we can talk about the numerical solution that you can use to solve it.

BTW- The Euler method you describe is often a very bad choice for solving tightly coupled stiff equations. Also, The Lagrangian method is a way to derive the equations of motion, not solving them. You can derive the equations of motion directly using Newton's laws, but this becomes very cumbersome.
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BigBad
Tue Mar 19 2013, 09:15PM
BigBad Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
Location:
Posts: 600
It's not very cumbersome for this particular problem, we know where the rotors are in space, their spin-speed and so forth.

And I don't see any evidence that it's stiff either.
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Steve Conner
Wed Mar 20 2013, 11:04AM
Steve Conner Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706
This is all very well, but Patrick has the pivots for his rotors set at 45 degrees to the axis of the airframe, so the effect of the gyroscopic torques will be different to all the other bicopters out there. My head asplode! Why did you do that Patrick? tongue
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