- #1
dgreenheck
- 23
- 0
I am doing an analysis concerning the torque-free motion of an axisymmetric body (J1 = J2 != J3).
The angular velocity is given
[itex]\omega(t) = [\omega_t\ sin(\Omega t), \omega_t\ cos(\Omega t), \omega_{z0}][/itex]
where [itex]\omega_t[/itex], [itex]\Omega[/itex] and [itex]\omega_{z0}[/itex] are constants. I would like to determine the orientation of the body at any time [itex]t[/itex] given an initial orientation at [itex]t = 0[/itex]. My end goal is to have an analytic representation of the orientation that I can use as "truth" to compare the errors of various numerical methods of estimating the orientation.
I know how to find numerical solutions to this problem using quaternions/direction cosine matrices/rotation vectors, etc., but am not sure how to approach this from an analytic point of view.
The angular velocity is given
[itex]\omega(t) = [\omega_t\ sin(\Omega t), \omega_t\ cos(\Omega t), \omega_{z0}][/itex]
where [itex]\omega_t[/itex], [itex]\Omega[/itex] and [itex]\omega_{z0}[/itex] are constants. I would like to determine the orientation of the body at any time [itex]t[/itex] given an initial orientation at [itex]t = 0[/itex]. My end goal is to have an analytic representation of the orientation that I can use as "truth" to compare the errors of various numerical methods of estimating the orientation.
I know how to find numerical solutions to this problem using quaternions/direction cosine matrices/rotation vectors, etc., but am not sure how to approach this from an analytic point of view.