Hamiltonian Dynamics of the Symmetric Top in External Axially-Symmetric Fields. Magnetic Retention of a Rigid Body

2018 ◽  
Vol 50 (7) ◽  
pp. 48-69
Author(s):  
Stanislav S. Zub
Keyword(s):  
Rigid Body ◽  
Hamiltonian Dynamics ◽  
Axially Symmetric ◽  
Magnetic Retention

Algorithm of the Time-Optimal Reorientation of an Axially Symmetric Spacecraft in the Class of Conical Motions

2018 ◽  
Vol 19 (12) ◽  
pp. 10-17587/mau.19.797-805
Author(s):  
Ya. G. Sapunkov ◽  
A. V. Molodenkov ◽  
T. V. Molodenkova
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Velocity Vector ◽  
Space Shuttle ◽  
Control Function ◽  
Axially Symmetric ◽  
Bounded Control ◽  
Angular Velocity Vector ◽  
Time Optimal ◽  
Optimal Turn

The problem of the time-optimal turn of a spacecraft as a rigid body with one axis of symmetry and bounded control function in absolute value is considered in the quaternion statement. For simplifying problem (concerning dynamic Euler equations), we change the variables reducing the original optimal turn problem of axially symmetric spacecraft to the problem of optimal turn of the rigid body with spherical mass distribution including one new scalar equation. Using the Pontryagin maximum principle, a new analytical solution of this problem in the class of conical motions is obtained. Algorithm of the optimal turn of a spacecraft is given. An explicit expression for the constant in magnitude optimal angular velocity vector of a spacecraft is found. The motion trajectory of a spacecraft is a regular precession. The conditions for the initial and terminal values of a spacecraft angular velocity vector are formulated. These conditions make it possible to solve the problem analytically in the class of conical motions. The initial and the terminal vectors of spacecraft angular velocity must be on the conical surface generated by arbitrary given constant conditions of the problem. The numerical example is presented. The example contain optimal reorientation of the Space Shuttle in the class of conical motions.

scholarly journals Hamiltonian dynamics of a rigid body in a central gravitational field

1990 ◽  
Vol 50 (4) ◽  
pp. 349-386 ◽  
Author(s):  
Li-Sheng Wang ◽  
P. S. Krishnaprasad ◽  
J. H. Maddocks
Keyword(s):  
Gravitational Field ◽  
Rigid Body ◽  
Hamiltonian Dynamics ◽  
Central Gravitational Field
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