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On some aspects of dynamics, modelling, and attitude analysis of satellites

University of British Columbia

The thesis identifies several limitations in the modelling and attitude stability analysis of two classes of spacecraft: rigid and flexible satellites. Attractive methods are proposed which promise to have far reaching consequences in spacecraft dynamics. These alternatives, developed based on techniques of differential equations, classical mechanics, and differential topology, are indicated below. (a) An Alternate Transition from the Lagrangian of a Satellite to Equations of Motion The classical procedure requires the Lagrangian to be expressed in terms of the corresponding generalized coordinates of the problem. This requirement significantly complicates the derivation of the equations of motion through an introduction of a set of librational generalized coordinates, which is strictly not a part of the dynamical system. Using the Lagrangian in the natural variables (angular velocity, direction cosines, and vibrational coordinates), one develops a procedure for derivation of equations of motion without an a priori choice of rotational generalized coordinates. For the case of a satellite with two flexible plate-type appendages, for example, the approach reduced the formulation time to one-third. (b) Synthesis and Depiction of Rotational Motion of Satellites and Robots The rotational coordinates in use for numerical prediction of orientation of a satellite are either singular or redundant. Furthermore, they lack a convenient visual interpretation. A new set of coordinates is proposed and an associated representation is developed which avoids these limitations. The procedure is applied to represent and integrate numerically the librational response of the flexible satellite mentioned in (a). (c) Resolution of Attitude Stability of Delp Satellites The development here tackles a long outstanding problem in the area of attitude stability of satellites. The resolution of this problem through normalization of the Hamiltonian leads to a better appreciation of stability associated with the class of gravity gradient structures such as the proposed Space Station.

Text

2010-10-07

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http://hdl.handle.net/2429/29019

Mechanical Engineering

University of British Columbia

Graduate