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The pendulum fallacy is the belief that rockets would be passively stable with engines at the top, with the rocket "hanging" from them. The error lies in expecting gravity to pull the body of the rocket down while the engines pull it up. In reality, gravity acts on the body of the rocket and the engines equally, exerting no torque (except for ...

24

In the inverted pendulum problem: gravity exerts a vertical force on the pendulum, at the center of gravity the support of the pendulum (like the finger under the pencil) exerts a vertical force on the pendulum, at the bottom of it In a rocket: gravity is the same engines exert a force along the long axis of the rocket, where the engine is (which doesn't ...

7

Discrete Fourier techniques introduce errors in their terms that track with the sinc function. Any target in the image will produce side lobes like those in the following graph. Strong reflections will create side lobes that have a higher amplitude than the background of the image. This is why the target appears to have a larger spatial extent than it ...

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I believe I have worked out my own question using http://www.dept.aoe.vt.edu/~cdhall/courses/aoe4140/attde.pdf This uses the TRIAD algorithim in order to determine a rotation matrix between the body and inertial frames by knowing two vectors in both frames. Usefully, it also weights one as being more accurate than the other which in this case is likely to be ...

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...ensure the center of gravity is behind the point generating thrust Should read center of drag is behind the center of gravity relative to the direction of flight. In the air, rockets follow the same directional stability rules as their aircraft cousins, and indeed, arrows. Putting a crude stick on a rocket will increase its drag but enhance its ...

1

My controls professor, Dr. Carroll Johnson at UAH, taught the rocket problem by first demonstrating the "try to balance a pencil on it's point" device. He then went on to have us attempt to stabilize a rocket system with various control techniques. The first exercise made a lot of unrealistic assumptions (no wind, perfect balance, etc.) just to ...

1

Tessarines are quite like numbers, and quaternions are more like 3D vectors plus one more special dimension. It is natural that vectors are useful in kinematics. On the other hand, split-complex numbers are related to Minkowski space, so if space farers ever need extensive calculations in special relativity, split numbers may be of use.

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