Papers by Annie Lyn Arias
As they tumble through space, objects like spacecraft move in dynamical ways. Understanding and p... more As they tumble through space, objects like spacecraft move in dynamical ways. Understanding and predicting the equations that represent that motion is critical to the safety and efficacy of spacecraft mission development. Kinetics: Modeling the Motions of Spacecraft trains knowledge in rigid body angular momentum and kinetic energy expression shown in a coordinate frame agnostic manner, single and dual rigid body systems tumbling without the forces of external torque, how differential gravity across a rigid body is approximated to the first order to study disturbances in both the attitude and orbital motion, and how these systems change when general momentum exchange devices are introduced.
*Derive from basic angular momentum formulation the rotational equations of motion and predict and determine torque-free motion equilibria and associated stabilities
* Develop equations of motion for a rigid body with multiple spinning components and derive and apply the gravity gradient torque
* Apply the static stability conditions of a dual-spinner configuration and predict changes as momentum exchange devices are introduced
* Derive equations of motion for systems in which various momentum exchange devices are present
In making observations of the sun and the stars, the surveyor is not interested in the distance o... more In making observations of the sun and the stars, the surveyor is not interested in the distance of the celestial bodies from the earth but merely in their angular positions. It is convenient to imagine their being attached to the inner surface of a hollow sphere of infinite radius of which the earth is the center. The imaginary sphere is the celestial sphere. The portion of the celestial sphere seen by the observer is the hemisphere above the plane of his own horizon. The reference plane passes through the center of the earth parallel with the observer's horizon, but the radius of the earth is so small in relation to the distances to the stars. Figure 1 represents the celestial sphere. Figure 1. Celestial Sphere Zenith Nadir North North Celestial Pole South Celestial Pole O DEFINITION OF TERMS Celestial Polesare the points on the earth's surface of the celestial sphere pierced by the extension of the earth's polar axis. Celestial Axis-is the prolongation of the earth's polar axis. Zenith-is the point where the plumb line at the place of observation projected above the horizon meets the celestial sphere. It is also defined on the celestial sphere vertically above the observer. Nadir-is that point on the celestial sphere directly beneath the observer, and directly opposite the zenith. Great Circle-a great circle of a sphere is the trace in its surface of the intersection of a plane passing through the center of the sphere. Observer's Horizon-a great circle on the sphere where a plane perpendicular through a plumb line at the place of observation and passing through the center of the earth, cuts the celestial sphere. Observer's Vertical-a vertical line at the location of the observer which coincides with the plumb line and is normal to the observer's horizon. Celestial Equator-a great circle which is perpendicular to the polar axis of the celestial sphere. It is an extension on the plane of the earth's equator outward until it intersects the celestial sphere. Vertical Circle-a great circle passing through the observer's zenith and any celestial body. Such a circle is perpendicular to the horizon, and represents the line of intersection of a vertical plane with the celestial sphere. Hour Circle-a great circle passing through a celestial body and whose plane is perpendicular to the plane of the celestial equator. Meridian-is the great circle of the celestial sphere which passes through the celestial poles and the observer's zenith. This circle is both a vertical and an hour circle. The position of any point on the surface the sphere may be fixed by angular measurements from two planes of reference at right angles to each other passing through the center of the sphere; these measurements are called the spherical coordinates of the point.
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Papers by Annie Lyn Arias
*Derive from basic angular momentum formulation the rotational equations of motion and predict and determine torque-free motion equilibria and associated stabilities
* Develop equations of motion for a rigid body with multiple spinning components and derive and apply the gravity gradient torque
* Apply the static stability conditions of a dual-spinner configuration and predict changes as momentum exchange devices are introduced
* Derive equations of motion for systems in which various momentum exchange devices are present
*Derive from basic angular momentum formulation the rotational equations of motion and predict and determine torque-free motion equilibria and associated stabilities
* Develop equations of motion for a rigid body with multiple spinning components and derive and apply the gravity gradient torque
* Apply the static stability conditions of a dual-spinner configuration and predict changes as momentum exchange devices are introduced
* Derive equations of motion for systems in which various momentum exchange devices are present