A complex analytic solution for the attitude motion of a near-symmetric rigid body under body-fixed torques

1991 ◽  
Vol 51 (3) ◽  
pp. 281-301 ◽  
Author(s):  
P. Tsiotras ◽  
J. M. Longuski
Keyword(s):  
Rigid Body ◽  
Analytic Solution ◽  
Attitude Motion ◽  
Symmetric Rigid Body

Analytical Solutions for a Spinning Rigid Body Subject to Time-Varying Body-Fixed Torques, Part I: Constant Axial Torque

1993 ◽  
Vol 60 (4) ◽  
pp. 970-975 ◽  
Author(s):  
J. M. Longuski ◽  
P. Tsiotras
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Analytic Solutions ◽  
Axisymmetric Body ◽  
Attitude Motion ◽  
Time Varying ◽  
Torque Vector ◽  
Constant Torque ◽  
Symmetric Rigid Body ◽  
Body Subject

Analytic solutions are derived for the general attitude motion of a near-symmetric rigid body subject to time-varying torques in terms of certain integrals. A methodology is presented for evaluating these integrals in closed form. We consider the case of constant torque about the spin axis and of transverse torques expressed in terms of polynomial functions of time. For an axisymmetric body with constant axial torque, the resulting solutions of Euler’s equations of motion are exact. The analytic solutions for the Eulerian angles are approximate owing to a small angle assumption, but these apply to a wide variety of practical problems. The case when all three components of the external torque vector vary simultaneously with time is much more difficult and is treated in Part II.

Analytic Solutions for a Spinning Rigid Body Subject to Time-Varying Body-Fixed Torques, Part II: Time-Varying Axial Torque

1993 ◽  
Vol 60 (4) ◽  
pp. 976-981 ◽  
Author(s):  
P. Tsiotras ◽  
J. M. Longuski
Keyword(s):  
Rigid Body ◽  
Analytic Solutions ◽  
Attitude Motion ◽  
Time Varying ◽  
General Attitude ◽  
Symmetric Rigid Body ◽  
Three Body ◽  
Body Subject

In this paper we extend the methodology developed in Part I in order to accommodate the case of an axial time-varying torque (in addition to the two transverse timevarying torques) acting on a rotating rigid body. The analytic solutions thus derived describe the general attitude motion of a near-symmetric rigid body subject to timevarying torques about all three body-fixed axes.

Note on free symmetric rigid body motion

2015 ◽  
Vol 20 (3) ◽  
pp. 293-308
Author(s):  
Vladimir Dragović ◽  
Borislav Gajić ◽  
Božidar Jovanović
Keyword(s):  
Rigid Body ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Symmetric Rigid Body
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