This paper presents an efficient treatment of gyroscopic bodies in the recursive solution of the dynamics of an $N$-body system. The bodies of interest include the reaction wheels in satellites, wheels on a car, and flywheels in machines. More specifically, these bodies have diagonal inertia tensors. They spin about one of its principal axes, with the moment of inertia along the transverse axes identical. Their center of mass lies on the spin axis. Current recursive solution methods treat these bodies identically as any other body in the system. The proposition here is that a body with gyroscopic children can be collectively treated as a composite body in the recursive solution process. It will be shown that this proposition improves the recursive solution speed to the $order(N−m)$ where $m$ is the number of gyroscopic bodies in the system. A satellite with three reaction wheels is used to illustrate the proposition.

1.
Vereshchagin
,
A. F.
, 1974, “
Computer Simulation of the Dynamics of Complicated Mechanisms
,”
Eng. Cybern.
0013-788X,
12
(
6
), pp.
65
70
.
2.
Armstrong
,
A. A.
, 1979, “
Recursive Solution to the Equations of Motion of an N-Link Manipulator
,”
Proceedings of the Fifth World Congress on Theory of Machines and Mechanisms
,
ASME
,
New York
.
3.
Hollerbach
,
J. M.
, 1980, “
A Recursive Lagrangian Formulation of Manipulator Dynamics and a Comparative Study of Dynamics Formulation Complexity
,”
IEEE Trans. Syst. Man Cybern.
0018-9472,
10
(
11)
, pp.
730
736
.
4.
Featherstone
,
R.
, 1983, “
The Calculation of Robotic Dynamics Using Articulated Body Inertias
,”
Int. J. Robot. Res.
0278-3649,
2
(
1
), pp.
13
30
.
5.
Rodriguez
,
G.
, 1986, “
Kalman Filtering, Smoothing and Recursive Robot Arm Forward and Inverse Dynamics
,”
IEEE J. Rob. Autom.
0882-4967,
RA-3
(
6
), pp.
624
639
.
6.
Bae
,
D. S.
, and
Haug
,
E. J.
, 1987, “
A Recursive Formulation for Constrained Mechanical System Dynamics: Part II, Closed Loop Systems
,”
Mech. Struct. Mach.
0890-5452,
15
, pp.
481
506
.
7.
Rosenthal
,
D.
, 1988, “
Order N Formulation for Equations of Motion of Multibody Systems
,”
Proceedings of the Workshop on Multibody Simulation
, Vol.
3
, pp.
1122
1150
, JPL Paper No. D-5190.
8.
Kane
,
T. R.
, 1961, “
Dynamics of Non-Holonomic Systems
,”
J. Appl. Mech.
0021-8936,
28
, pp.
574
578
.
9.
Hooker
,
W. W.
, and
Margulies
,
G.
, 1965, “
The Dynamical Attitude Equations for an n-Body Satellite
,”
J. Astronaut. Sci.
0021-9142,
12
(
4
), pp.
123
128
.
10.
Russell
,
W. J.
, 1969, “
On the Formulation of Equations of Rotational Motion for an N-Body Spacecraft
,”
Aerospace
, El Segundo, Paper No. TR-0200 (4133).
11.
Likins
,
P. W.
, 1974, “
Analytical Dynamics and Nonrigid Spacecraft Simulation
,”
Jet Propulsion Laboratory
, Technical Report No. 32-1593.
12.
Likins
,
P. W.
, 1975, “
Point-Connected Rigid Bodies in a Topological Tree
,”
Celest. Mech.
0008-8714,
11
(
3
), pp.
301
317
.
13.
Ho
,
J. Y. L.
, 1977, “
Direct Path Method for Flexible Multibody Spacecraft Dynamics
,”
J. Spacecr. Rockets
0022-4650,
14
, pp.
102
110
.
14.
Wittenburg
,
J.
, 1977,
Dynamics of Systems of Rigid Bodies
,
G. G. Teubener
,
Stuttgart
.
15.
Jerkovsky
,
W.
, 1978, “
The Structure of Multibody Dynamics Equations
,”
J. Guid. Control
0162-3192,
3
(
1
), pp.
730
736
.
16.
Bodley
,
C. S.
,
Devers
,
A. D.
,
Park
,
A. C.
, and
Frisch
,
H. P.
, 1978, “
A Digital Computer Program for the Dynamic Interaction Simulation of Controls and Structures (DISCOS)
,” NASA Technical Paper No. 1219, Vol.
1
.
17.
Kane
,
T. R.
,
Likins
,
P. W.
, and
Levinson
,
D. A.
, 1983,
Spacecraft Dynamics
,
McGraw-Hill
,
New York
.
18.
Hughes
,
P. C.
, 1986,
Spacecraft Attitude Dynamics
,
Wiley
,
New York
19.
Robertson
,
R. E.
, and
Schwertassek
,
R.
, 1988,
Dynamics of Multibody Systems
,
Springer-Verlag
,
Berlin
.
20.
Haug
,
E. J.
, 1989,
Computer Aided Kinematics and Dynamics of Mechanical Systems
,
Allyn and Bacon
,
Boston
.
21.
Schiehlen
,
W.
, 2006, “
Computational Dynamics: Theory and Applications of Multibody Systems
,”
Eur. J. Mech. A/Solids
0997-7538,
25
, pp.
566
594
.
22.
Franklin
,
J. N.
, 1968,
Matrix Theory
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
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