Perfect and Imperfect Collinearity in Multibody Gyro Systems

The behaviour of multibody gyroscopic systems is governed by the collinearity principle. In the present paper the collinearity principle is stated and its origin, history and applications are discussed. It is then used in two examples of spacecraft with momentum wheels to demonstrate its validity and applicability

Open Orbits in Satellite Dynamics

Recent investigations into the effects of a constant atmospheric drag force on an essentially circular satellite orbit have led to an analytical expression for the resulting orbit, which is obviously not exactly circular, but so close to it that profitable simplifications can be made in its derivation. In the present paper several of the resulting type orbits are analyzed and compared

Canonical Equations in Terms of Generalized Impulse Variables

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Planet Absorption by a Gas Giant

There is mounting evidence of many extra-solar planetary systems in our galaxy, consisting typically of a Sun-like star and Jupiter-like planets on highly elliptic orbits. These systems are characterised by a dearth of smaller Earth-like planets. The present paper describes the swallowing-up of a small rock dwarf by a large gas giant, and shows that this behaviour is as predicted by the collinearity principle

A Note on Hohmann Transfer Velocity Kicks

A Hohmann transfer is a well-known spacecraft manoeuvre, initiated by a horizontal velocity kick Δv1, which effects a change from an original, say, circular orbit to the Hohmann transfer ellipse in its perigee, and completed by a second horizontal velocity kick Δv2 in the apogee, to eflect a change from the transfer ellipse to a final, say, larger circular orbit.A velocity kick as mentioned above is apparently instantaneous, and free of any side effects, a very idealized concept, which, as it turns out, isfar removedfrom reality.Recent investigations into Ward spirals have shed some light into how velocity changes can be brought about. It is shown that a vertical impulse component must be present to accompany a horizontal impulse in order to assure that the altitude remains constant during a horizontal velocity change

On the Disintegration of Very Small Satellites

Small Satellites will disintegrate, if they find a means, such as a separation force, to do so. If inside their Roche limit they are indeed subject to a separation force, that might be sufificient to bring about fragmentation. It is shown in the present paper that satellite disintegration leads to a reduction of orbital energy. The result can be looked upon as a generalization of the collinearity principle, according to which planetary systems strive towards a minimum energy state, for a given constant angular momentum

Complementary Formulation of the Appell Equation

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Attitude Diagrams for the Description of the Attitude Drift of Torquefree Asymmetric Gyros

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Galactic Contraction and the Collinearity Principle

In a spiral galaxy there is not only a Kepler force acting on an individual star but also a transverse pail opposing the motion. The relatively small transverse pall is due to the atmospheric drag exerted by interstellar gas (hydrogen, cosmic dust). It is also shown that the arms of a spiral galaxy consist of Ward spirals, that there is an orbital energy loss for each individual star in a contracting galaxy, and that the size of the Ward spiral observed can be used to predict the speed of the galaxy’s contracting. For inside the galaxy’s central sphere it is shown that the path of a star describes a logarithmic spiral and that there is an associated orbital energy loss

Angular Momentum Collinearization of an Elastic Gyro with Hysteresis

In the present paper it is shown in some detail how the energy dissipation in a deforming elastic gyro leads to a collinearization of the angular momenta, according to the collinearity principle