Root
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Conference Proceedings
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6th EUROMECH Nonlinear Dynamics Conference (ENOC 2008)
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Steady motions of a tetrahedral satellite
with tethered elements
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The procedure of the Routh reduction is well-known for systems of

Lagrangian equations in the case, when one or few generalized

coordinates are cyclic. However, if this system admits a symmetry

group given by a vector field on the configuration space, but the

cyclic coordinates are not given explicitly, the reduction seems

difficult. Here we describe the reduction in this case.

The result is applied to the problem of motion of a system of

interacting material points moving about an attracting center. In

particular, the expression for the amended potencial is obtained by

the proposed procedure without introduction of any special

coordinates.

The obtained potential is used to analise the stationary motions of

a tetrahedral satellite in a central Newtonian gravitational field.

The tetrahedral structure is assumed to be regular; it is composed

by rigid and tether elements. The possibility to use flexible

tethers to provide a stationary tetrahedral configuration is

discussed. The structure possesses spherically symmetric tensor of

inertia, so we use the Routh method with the amended potential. The

reactions in the links are studied using Lagrangian multipliers. The

goal is to identify the stretched links so they could be replaced by

massless inextensible tethers.

Lagrangian equations in the case, when one or few generalized

coordinates are cyclic. However, if this system admits a symmetry

group given by a vector field on the configuration space, but the

cyclic coordinates are not given explicitly, the reduction seems

difficult. Here we describe the reduction in this case.

The result is applied to the problem of motion of a system of

interacting material points moving about an attracting center. In

particular, the expression for the amended potencial is obtained by

the proposed procedure without introduction of any special

coordinates.

The obtained potential is used to analise the stationary motions of

a tetrahedral satellite in a central Newtonian gravitational field.

The tetrahedral structure is assumed to be regular; it is composed

by rigid and tether elements. The possibility to use flexible

tethers to provide a stationary tetrahedral configuration is

discussed. The structure possesses spherically symmetric tensor of

inertia, so we use the Routh method with the amended potential. The

reactions in the links are studied using Lagrangian multipliers. The

goal is to identify the stretched links so they could be replaced by

massless inextensible tethers.