Roll Dynamics of a Spinning Axi-Symmetric Satellite in an Elliptic Orbit

1968 ◽  
Vol 72 (696) ◽  
pp. 1061-1065 ◽  
Author(s):  
V. J. Modi ◽  
J. E. Neilson
Keyword(s):  
Asymptotic Analysis ◽  
Rigid Body ◽  
Numerical Solution ◽  
Linear Systems ◽  
Equations Of Motion ◽  
Elliptic Orbit ◽  
Attitude Dynamics ◽  
Circular Trajectory ◽  
Symmetric Rigid Body ◽  
Non Linear Systems

Attitude dynamics of a spinning, axi-symmetric, rigid body undergoing central force motion has received considerable attention in recent times. Thomson et al studied the problem where the satellite was restricted to follow a circular trajectory. This stipulation reduced the system to an autonomous form which was then treated by linearised or Liapounov type of analysis. For the satellite in an elliptic orbit, Kane and Barba presented numerical solution to the linearised equations of motion. Recently Wallace and Meirovitch investigated the same problem by performing asymptotic analysis on linear and low order non-linear systems.

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.

Asymptotic analysis of almost periodic weakly non-linear systems

1991 ◽  
Vol 54 (3) ◽  
pp. 561-575
Author(s):  
MOHAMED EL-GEBEILY ◽  
KAMAL A. F. MOUSTAFA
Keyword(s):  
Asymptotic Analysis ◽  
Linear Systems ◽  
Almost Periodic ◽  
Non Linear ◽  
Non Linear Systems

Holomorphically projective mappings between generalized m-parabolic Kähler manifolds

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4865-4873 ◽  
Author(s):  
Milos Petrovic
Keyword(s):  
Linear Systems ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Covariant Derivatives ◽  
Linearly Independent ◽  
Non Linear ◽  
Non Linear Systems ◽  
Curvature Tensors ◽  
Derivatives Of

Generalized m-parabolic K?hler manifolds are defined and holomorphically projective mappings between such manifolds have been considered. Two non-linear systems of PDE?s in covariant derivatives of the first and second kind for the existence of such mappings are given. Also, relations between five linearly independent curvature tensors of generalized m-parabolic K?hler manifolds with respect to these mappings are examined.

Distributed track‐to‐track fusion for non‐linear systems with Gaussian mixture noise

2019 ◽  
Vol 13 (5) ◽  
pp. 740-749 ◽  
Author(s):  
Kelin Lu ◽  
Changyin Sun ◽  
Qien Fu ◽  
Qian Zhu
Keyword(s):  
Linear Systems ◽  
Gaussian Mixture ◽  
Track Fusion ◽  
Non Linear ◽  
Non Linear Systems
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