Static determinacy of the limiting state of a rigid body subject to separation

1996 ◽  
Vol 32 (6) ◽  
pp. 450-453
Author(s):  
D. D. Ivlev
Keyword(s):  
Rigid Body ◽  
Limiting State ◽  
Static Determinacy ◽  
Body Subject

The Global Motion of a Rigid Body Subject to Periodic Body-Fixed Torques

1995 ◽  
Author(s):  
X. Tong ◽  
B. Tabarrok
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Melnikov Method ◽  
The Body ◽  
Body Motion ◽  
Heteroclinic Orbits ◽  
Coordinate Frame ◽  
Global Motion ◽  
Stable And Unstable Manifolds ◽  
Body Subject

Abstract In this paper the global motion of a rigid body subject to small periodic torques, which has a fixed direction in the body-fixed coordinate frame, is investigated by means of Melnikov’s method. Deprit’s variables are introduced to transform the equations of motion into a form describing a slowly varying oscillator. Then the Melnikov method developed for the slowly varying oscillator is used to predict the transversal intersections of stable and unstable manifolds for the perturbed rigid body motion. It is shown that there exist transversal intersections of heteroclinic orbits for certain ranges of parameter values.

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.

COMPUTER CODE FOR THE IN-CLASS STUDY OF THE EQUILIBRIUM OF A RIGID BODY SUBJECT TO CONSTRAINTS

2019 ◽  
Author(s):  
Andrei Craifaleanu ◽  
Cristian Dragomirescu ◽  
Iolanda-Gabriela Craifaleanu
Keyword(s):  
Rigid Body ◽  
Computer Code ◽  
Body Subject

Analytical Solutions for Translational Motion of Spinning-Up Rigid Bodies Subject to Constant Body-Fixed Forces and Moments

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
Mohammad A. Ayoubi ◽  
James M. Longuski
Keyword(s):  
Rigid Body ◽  
Numerical Simulations ◽  
Closed Form ◽  
Analytical Solutions ◽  
Translational Motion ◽  
Rigid Bodies ◽  
Spin Axis ◽  
Transverse Displacement ◽  
Fixed Direction ◽  
Body Subject

The problem of a spinning, axisymmetric, or nearly axisymmetric rigid body subject to constant body-fixed forces and moments about three axes is considered. Approximate closed-form analytical solutions are derived for velocity and for the transverse displacement. The analytical solutions are valid when the excursion of the spin axis with respect to an inertially fixed direction is small (which is usually the case for spin-stabilized spacecraft and rockets). Numerical simulations confirm that the solutions are highly accurate when applied to typical motion of a spacecraft, such as the Galileo.

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.

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