Summary

Summary of this folder PhL 3.26.17 I wasted a whole day on this little study which I will now explain was done completely wrong, so all the other docs in this folder are completely wrong. MAIN POINT First, my Appendix I on Rigid Body Dynamics makes use of two reference Frames, one of which is embedded into the rotating object of interest. As I say in the very first line: 1.1 The Appearance of the Inertia Tensor Assume that Frame S' is embedded into a rigid body, so that Frame S' and that rigid body are rotating at I go on in that Appendix I to develop equations of motion for a rigid body in such a situation, (N)'1 = I'1 ()'1 - (ω)'2(ω)'3 (I'2 - I'3) (N)'2 = I'2 ()'2 - (ω)'3(ω)'1 (I'3 - I'1) (N)'3 = I'3 ()'3 - (ω)'1(ω)'2 (I'1 - I'2) . (I.4.3) These are the "rigid body equations of motion" in body frame components, where I have already chosen the body frame axes to diagonalize the inertia tensor. Now we change the scene. In Appendix F I analyze the dumbbell satellite problem. In that problem, one Frame of reference is in orbit going around the earth. This is a non-inertial frame. A second frame is embedded into a non-rotating Earth. Neither of these frames is embedded into the rotating dumbbell body, so in Appendix F neither frame is the body frame of the dumbbell!!!!! Thus, the equations (I.4.3) I show above having nothing at all to do with the dumbbell satellite problem!! So all my work in the three docs in this folder is meaningless! HOW WOULD YOU DO A RIGID BODY ANALYSIS? I think this would be quite a pain to do. You would need a third Frame perhaps Frame S" which is embedded into the dumbbell. Then Frame S is the sky frame that is also non-inertial and Frame S' is the ground inertial frame. Suppose then we consider only the two non-inertial frames S" embedded into rotor, and S in the sky. I think you could go ahead and write L = Iω and have the usual Iij which you could evaluate in any frame. I don't think anything in Section I.2 requires that Frame S be inertial, which is good since it is non-inertial. But then I say : From (11.3.2) Newton's Second Law (angular motion) applied in inertial Frame S states, N = // = ∂SL = (dL/dt)S (I.2.1) This would not be true in the sky frame S, so the resulting (I.4.3) would be invalid,. Conclusion: To do this problem right, you have to manage THREE frames of reference. Then you use frames doc to establish how each pair of frames is related. You might try to use Neff = for the sky frame S where you include a fictitious force to account for the fact that the sky frame is non-inertial. You end up with some equations of motion which is different from the set (I.4.3) above. I really have no interest in attempting this problem at this time.